Statistica Sinica: Volume 28, Number 3, July 2018This is an example of an RSS feedhttp://www3.stat.sinica.edu.tw/statistica/Wed, 20 June 2018 00:01:00 +0000 Wed, 20 June 2018 00:01:00 +00001800
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CLUSTERS WITH UNEQUAL SIZE: MAXIMUM LIKELIHOOD VERSUS WEIGHTED ESTIMATION IN LARGE SAMPLES Lisa Hermans, Vahid Nassiri, Geert Molenberghs,Michael G. Kenward, Wim Van der Elst, Marc Aerts and Geert Verbeke 1107-1132<span style='font-size=12pt;'><center>Abstract</center> The analysis of hierarchical data that take the form of clusters with random size has received considerable attention. The focus here is on samples that are very large in terms of number of clusters and/or members per cluster, on the one hand, as well as on very small samples (e.g., when studying rare diseases), on the other. Whereas maximum likelihood inference is straightforward in medium to large samples, in samples of sizes considered here it may be prohibitive. We propose sample-splitting (Molenberghs, Verbeke and Iddi (2011)) as a way to replace iterative optimization of a likelihood that does not admit an analytical solution, with closed-form calculations. We use pseudo-likelihood (Molenberghs et al. (2014)), consisting of computing weighted averages over solutions obtained for each cluster size occurring. As a result, the statistical properties of this approach need to be investigated, especially because the minimal sufficient statistics involved are incomplete. The operational characteristics were studied using simulations. Simulations were also done to compare the proposed method to existing techniques developed to circumvent difficulties with unequal cluster sizes, such as multiple imputation. It follows that the proposed non-iterative methods have a strong beneficial impact on computation time; at the same time, the method is the most precise among its competitors considered. The findings are illustrated using data from a developmental toxicity study, where clusters are formed of fetuses within litters.<p>Key words and phrases: Likelihood inference, pseudo-likelihood, unequal cluster size.</span>
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A FURTHER STUDY OF PROPENSITY SCORE CALIBRATION IN MISSING DATA ANALYSIS Peisong Han 1307-1332<span style='font-size=12pt;'><center>Abstract</center> Methods for propensity score (PS) calibration are commonly used in missing data analysis. Most of them are derived based on constrained optimizations where the form of calibration is dictated by the objective function being optimized and the calibration variables used in the constraints. Considerable efforts on pairing an appropriate objective function with the calibration constraints are usually needed to achieve certain efficiency and robustness properties for the final estimators. We consider an alternative approach where the calibration is carried out by solving the empirical version of certain moment equalities. This approach frees us from constructing a particular objective function. Based on this approach, under the setting of estimating the mean of a response, we establish intrinsic, improved and local efficiency and multiple robustness in the presence of multiple data distribution models. A revisit to the generalized pseudo exponential tilting estimator and generalized pseudo empirical likelihood estimator of Tan and Wu (2015) is also provided. <p>Key words and phrases: Calibration, efficiency, empirical likelihood, missing at random (MAR), multiple robustness, propensity score.</span>
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SEMIPARAMETRIC RANDOM-EFFECTS CONDITIONAL DENSITY MODELS FOR LONGITUDINAL ANALYSIS WITH CONCOMITANT INTERVENTION Tianqing Liu, Colin O. Wu, Zhaohai Li and Yuanzhang Li 1333-1349<span style='font-size=12pt;'><center>Abstract</center> Longitudinal data in biomedical studies often involve concomitant interventions in addition to the pre-specified repeatedly measured outcome and covariate variables. Since a concomitant intervention is often initiated when a patient exhibits an undesirable health trend, adequate statistical methods should properly incorporate the starting time of a concomitant intervention in order to reduce the potential bias of the estimated intervention effects. We propose in this paper a class of semiparametric random-effects conditional density models for evaluating the distributions and concomitant intervention effects with longitudinal observations. These models simultaneously incorporate concomitant intervention effects and intra-subject longitudinal dependence structures, and quantify the change of the distribution functions through the ratio of two conditional density functions. The conditional density ratio is assumed to have a parametric form, while the baseline density function is nonparametric. We develop a likelihood-based method for estimating the parameters and a goodness-of-fit test for testing the validity of the models. Finite sample properties of our estimation and testing procedures are illustrated through a simulation study and an application to a longitudinal clinical trial in depression and heart disease.<p>Key words and phrases: Concomitant intervention, conditional density ratio, conditional likelihood, longitudinal data, random-effects conditional density model.</span>
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MODEL-FREE FEATURE SCREENING FOR ULTRAHIGH DIMENSIONAL DATATHROUGH A MODIFIED BLUM-KIEFER-ROSENBLATT CORRELATION Yeqing Zhou and Liping Zhu 1351-1370<span style='font-size=12pt;'><center>Abstract</center> In this paper we introduce a modified Blum-Kiefer-Rosenblatt correlation (MBKR for short) to rank the relative importance of each predictor in ultrahigh-dimensional regressions. We advocate using the MBKR for two reasons. First, it is nonnegative and is zero if and only if two random variables are independent, indicating that the MBKR can detect nonlinear dependence. We illustrate that the sure independence screening procedure based on the MBKR (MBKR-SIS for short) is effective in detecting nonlinear effects, including interactions and heterogeneity, particularly when both continuous and discrete predictors are involved. Second, the MBKR is conceptually simple, easy to implement, and affine-invariant. It is free of tuning parameters and no iteration is required in estimation. It remains unchanged when order-preserving transformations are applied to the response or predictors, indicating that the MBKR-SIS is robust to the presence of extreme values and outliers in the observations. We show that, under mild conditions, the MBKR-SIS procedure has the sure screening and ranking consistency properties, guaranteeing that all important predictors can be retained after screening with probability approaching one. We also propose an iterative screening procedure to detect the important predictors that are marginally independent of the response variable. We demonstrate the merits of the MBKR-SIS procedure through simulations and an application to a dataset.<p>Key words and phrases: Blum-Kiefer-Rosenblatt correlation, feature screening, independence test, ranking consistency property, sure screening property.</span>
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AN ITERATIVE HARD THRESHOLDING ESTIMATOR FOR LOW RANK MATRIX RECOVERY WITH EXPLICIT LIMITING DISTRIBUTION Alexandra Carpentier and Arlene K. H. Kim 1371-1393<span style='font-size=12pt;'><center>Abstract</center> We consider the problem of low rank matrix recovery in a stochastically noisy high-dimensional setting. We propose a new estimator for the low rank matrix, based on the iterative hard thresholding method, that is computationally efficient and simple. We prove that our estimator is optimal in terms of the Frobenius risk and in terms of the entry-wise risk uniformly over any change of orthonormal basis, allowing us to provide the limiting distribution of the estimator. When the design is Gaussian, we prove that the entry-wise bias of the limiting distribution of the estimator is small, which is of interest for constructing tests and confidence sets for low-dimensional subsets of entries of the low rank matrix. <p>Key words and phrases: High dimensional statistical inference, inverse problem, limiting distribution, low rank matrix recovery, numerical methods, uncertainty quantification. </span>
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CONSTRUCTION OF MAXIMIN DISTANCE DESIGNS VIA LEVEL PERMUTATION AND EXPANSION Qian Xiao and Hongquan Xu 1395-1414<span style='font-size=12pt;'><center>Abstract</center> Maximin distance designs as an important class of space-filling designs are widely used in computer experiments, yet their constructions are challenging. We develop an efficient procedure to generate maximin Latin hypercube designs, as well as maximin multi-level fractional factorial designs, from existing orthogonal or nearly orthogonal arrays via level permutation and expansion. We show that the distance distributions of the generated designs are closely connected with the distance distributions and generalized word-length patterns of the initial designs. Examples are presented to show that our method outperforms many current prevailing methods. <p>Key words and phrases: Computer experiment, fractional factorial design, generalized minimum aberration, Latin hypercube design, orthogonal array, space-filling design.</span>
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CONSTRUCTION OF MAXIMIN DISTANCE DESIGNS VIA LEVEL PERMUTATION AND EXPANSION Qian Xiao and Hongquan Xu 1395-1414<span style='font-size=12pt;'><center>Abstract</center> In sufficient dimension reduction, the second-order inverse regression methods, such as the principal Hessian directions and directional regression, commonly require the predictor to be normally distributed. In this paper, we introduce a type of elliptical distributions called the quadratic variance ellipticity family, which covers and approximates a variety of commonly seen elliptical distributions, with the normal distribution as a special case. When the predictor belongs to this family, we study the properties of the second-order inverse regression methods and adjust them accordingly to preserve consistency. When the dimension of the predictor is sufficiently large, we show the consistency of the conventional methods, which strengthens a previous result in Li and Wang (2007). Simulation studies and data analysis are conducted to illustrate the effectiveness of the adjusted methods. <p>Key words and phrases: Central mean subspace, central subspace, directional regression, principal Hessian directions, quadratic variance ellipticity family.</span>
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CONSTRUCTION OF MAXIMIN DISTANCE DESIGNS VIA LEVEL PERMUTATION AND EXPANSION Qian Xiao and Hongquan Xu 1395-1414<span style='font-size=12pt;'><center>Abstract</center> Generally the Likelihood Ratio statistic Λ for standard hypotheses is asymptotically χ<sup>2</sup> distributed, and the Bartlett adjustment improves the χ<sup>2</sup> approximation to its asymptotic distribution in the sense of third-order asymptotics. However, if the parameter of interest is on the boundary of the parameter space, Self and Liang (1987) show that the limiting distribution of Λ is a mixture of χ<sup>2</sup> distributions. For such nonstandard setting of hypotheses, the present paper develops the third-order asymptotic theory for a class S of test statistics, which includes the Likelihood Ratio, the Wald, and the Score statistic, in the case of observations generated from a general stochastic process, providing widely applicable results. In particular, it is shown that Λ is Bartlett adjustable despite its nonstandard asymptotic distribution. Although the other statistics are not Bartlett adjustable, a nonlinear adjustment is provided for them which greatly improves the χ<sup>2</sup> approximation to their distribution and allows a subsequent Bartlett-type adjustment.Numerical studies confirm the benefits of the adjustments on the accuracy and on the power of tests whose statistics belong to S. <p>Key words and phrases: Bartlett adjustment, boundary parameter, high-order asymptotic theory, likelihood ratio test, nonstandard conditions, score test, Wald test.</span>
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EFFICIENT GAUSSIAN PROCESS MODELING USING EXPERIMENTAL DESIGN-BASED SUBAGGING Yibo Zhao, Yasuo Amemiya and Ying Hung 1459-1479<span style='font-size=12pt;'><center>Abstract</center> We address two important issues in Gaussian process (GP) modeling. One is how to reduce the computational complexity in GP modeling and the other is how to simultaneous perform variable selection and estimation for the mean function of GP models. Estimation is computationally intensive for GP models because it heavily involves manipulations of an 𝓃-by-𝓃 correlation matrix, where 𝓃 is the sample size. Conventional penalized likelihood approaches are widely used for variable selection. However the computational cost of the penalized likelihood estimation (PMLE) or the corresponding one-step sparse estimation (OSE) can be prohibitively high as the sample size becomes large, especially for GP models. To address both issues, this article proposes an efficient subsample aggregating (subagging) approach with an experimental design-based subsampling scheme. The proposed method is computationally cheaper, yet it can be shown that the resulting subagging estimators achieve the same efficiency as the original PMLE and OSE asymptotically. The finite-sample performance is examined through simulation studies. Application of the proposed methodology to a data center thermal study reveals some interesting information, including identifying an efficient cooling mechanism.<p>Key words and phrases: Bagging, computer experiment, experimental design, Gaussian process, Latin hypercube design, model selection.</span>
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BASELINE ZONE ESTIMATION IN TWO DIMENSIONS WITH REPLICATED MEASUREMENTS UNDER A CONVEXITY CONSTRAINT Atul Mallik, Moulinath Banerjee and Michael Woodroofe 1481-1502
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CONSTRUCTION OF ORTHOGONAL SYMMETRIC LATIN HYPERCUBE DESIGNS Lin Wang, Fasheng Sun, Dennis K. J. Lin and Min-Qian Liu 1503-1520<span style='font-size=12pt;'><center>Abstract</center> Latin hypercube designs (LHDs) have found wide application in computer experiments. It is known that orthogonal LHDs guarantee the orthogonality between all linear effects, and symmetric LHDs ensure the orthogonality between linear and second-order effects. In this paper, we propose a construction method for orthogonal symmetric LHDs. Most resulting LHDs can accommodate the maximum number of factors, thus can study many more factors than existing ones. Several methods for constructing nearly orthogonal symmetric LHDs are also provided. The constructed orthogonal and nearly orthogonal LHDs can be utilized to generate more nearly orthogonal symmetric LHDs. A detailed comparison with existing designs shows that the resulting designs have more flexible and economical run sizes, and many desirable design properties. <p>Key words and phrases: Computer experiment, correlation, second-order effect, symmetric Latin hypercube design.</span>
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ROBUST BOUNDED INFLUENCE TESTS FOR INDEPENDENT NON-HOMOGENEOUS OBSERVATIONS Abhik Ghosh and Ayanendranath Basu 1133-1155<span style='font-size=12pt;'><center>Abstract</center> Experiments often yield non-identically distributed data for statistical analysis. Tests of hypothesis under such set-ups are generally performed using the likelihood ratio test, which is non-robust with respect to outliers and model misspecification. In this paper, we consider the set-up of non-identically but independently distributed observations and develop a general class of test statistics for testing parametric hypothesis based on the density power divergence. The proposed tests have bounded influence functions, are highly robust with respect to data contamination, have high power against contiguous alternatives, and are consistent at any fixed alternative. The methodology is illustrated by the simple and generalized linear regression models with fixed covariates.<p>Key words and phrases: Generalized linear model, influence function, linear regression, non-homogeneous observation, robust testing of hypothesis.</span>
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ROBUST BOUNDED INFLUENCE TESTS FOR INDEPENDENT NON-HOMOGENEOUS OBSERVATIONS Abhik Ghosh and Ayanendranath Basu 1133-1155<span style='font-size=12pt;'><center>Abstract</center> Variable selection is central to sparse modeling, and many methods have been proposed under various model assumptions. Most existing methods are based on an explicit functional relationship, while we are concerned with a model-free variable selection method that attempts to identify informative variables that are related to the response by simultaneously examining the sparsity in multiple conditional quantile functions. It does not require specification of the underlying model for the response. The proposed method is implemented via an efficient computing algorithm that couples the majorize-minimization algorithm and the proximal gradient descent algorithm. Its asymptotic estimation and variable selection consistencies are established, without explicit model assumptions, that assure the truly informative variables are correctly identified with high probability. The effectiveness of the proposed method is supported by a variety of simulated and real-life examples. <p>Key words and phrases: Lasso, learning gradients, quantile regression, reproducing kernel Hilbert space (RKHS), sparsity, variable selection.</span>
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ROBUST BOUNDED INFLUENCE TESTS FOR INDEPENDENT NON-HOMOGENEOUS OBSERVATIONS Abhik Ghosh and Ayanendranath Basu 1133-1155<span style='font-size=12pt;'><center>Abstract</center> We propose a doubly robust estimation method for the optimal treatment regime based on an additive hazards model with censored survival data. Specifically, we introduce a new semiparametric additive hazard model which allows flexible baseline covariate effects in the control group and incorporates marginal treatment effect and its linear interaction with covariates. In addition, we propose a time-dependent propensity score to construct an A-learning type of estimating equations. The resulting estimator is shown to be consistent and asymptotically normal when either the baseline effect model for covariates or the propensity score is correctly specified. The asymptotic variance of the estimator is consistently estimated using a simple resampling method. Simulation studies conducted to evaluate the finite-sample performance of the estimators are reported, and an application to AIDS clinical trial data is given to illustrate the methodology. <p>Key words and phrases: A-learning estimating equations, additive hazards model, doubly robust, optimal treatment regime, time-dependent propensity score.</span>
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SPARSE ESTIMATION OF GENERALIZED LINEAR MODELS (GLM) VIA APPROXIMATED INFORMATION CRITERIA Xiaogang Su, Juanjuan Fan, Richard A. Levine, Martha E. Nunn and Chih-Ling Tsai 1561-1581<span style='font-size=12pt;'><center>Abstract</center> We propose a sparse estimation method, termed MIC (Minimum approximated Information Criterion), for generalized linear models (GLM) in fixed dimensions. What is essentially involved in MIC is the approximation of the 𝓁<sub>0</sub> -norm by a continuous unit dent function. A reparameterization step is devised to enforce sparsity in parameter estimates while maintaining the smoothness of the objective function. MIC yields superior performance in sparse estimation by optimizing the approximated information criterion without reducing the search space and is computationally advantageous since no selection of tuning parameters is required. Moreover, the reparameterization tactic leads to valid significance testing results free of post-selection inference. We explore the asymptotic properties of MIC, and illustrate its usage with simulated experiments and empirical examples. <p>Key words and phrases: Adaptive, breakdown point, least trimmed squares, outliers, penalized regression, robust regression, variable selection.</span>
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DERIVATIVE PRINCIPAL COMPONENT ANALYSIS FOR REPRESENTING THE TIME DYNAMICS OF LONGITUDINAL AND FUNCTIONAL DATA Xiongtao Dai, Hans-Georg Müller and Wenwen Tao 1583-1609<span style='font-size=12pt;'><center>Abstract</center> We propose a nonparametric method to explicitly model and represent the derivatives of smooth underlying trajectories for longitudinal data. This representation is based on a direct Karhunen-Loève expansion of the unobserved derivatives and leads to the notion of derivative principal component analysis, which complements functional principal component analysis, one of the most popular tools of functional data analysis. The proposed derivative principal component scores can be obtained for irregularly spaced and sparsely observed longitudinal data, as typically encountered in biomedical studies, as well as for functional data which are densely measured. Novel consistency results and asymptotic convergence rates for the proposed estimates of the derivative principal component scores and other components of the model are derived under a unified scheme for sparse or dense observations and mild conditions. We compare the proposed representations for derivatives with alternative approaches in simulation settings and also in a wallaby growth curve application. It emerges that representations using the proposed derivative principal component analysis recover the underlying derivatives more accurately compared to principal component analysis-based approaches especially in settings where the functional data are represented with only a very small number of components or are densely sampled. In a second wheat spectra classification example, derivative principal component scores were found to be more predictive for the protein content of wheat than the conventional functional principal componentscores. <p>Key words and phrases: Best linear unbiased prediction, derivatives, empirical dynamics, functional principal component analysis, growth curves.</span>
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DERIVATIVE PRINCIPAL COMPONENT ANALYSIS FOR REPRESENTING THE TIME DYNAMICS OF LONGITUDINAL AND FUNCTIONAL DATA Xiongtao Dai, Hans-Georg Müller and Wenwen Tao 1583-1609<span style='font-size=12pt;'><center>Abstract</center> Missing responses occur in many industrial and medical experiments, for example in clinical trials where slow acting treatments are assessed. Finding efficient designs for such experiments is problematic since it is not known at the design stage which observations will be missing. The design literature mainly focuses on assessing robustness of designs for missing data scenarios, rather than finding designs which are optimal in this situation. Imhof, Song and Wong (2002) propose a framework for design search, based on the expected information matrix. We develop an approach that includes Imhof, Song and Wong (2002)'s method as special case and justifies its use retrospectively. Our method is illustrated through a simulation study based on data from an Alzheimer's disease trial. <p>Key words and phrases: Covariance matrix, information matrix, linear regression model, missing observations, optimal design.</span>
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DERIVATIVE PRINCIPAL COMPONENT ANALYSIS FOR REPRESENTING THE TIME DYNAMICS OF LONGITUDINAL AND FUNCTIONAL DATA Xiongtao Dai, Hans-Georg Müller and Wenwen Tao 1583-1609<span style='font-size=12pt;'><center>Abstract</center> This paper considers a continuous time analogue of the classical autoregressive moving average processes, Lévy-driven CARMA processes. First we describe limiting properties of the periodogram by means of the so-called truncated Fourier transform if observations are available continuously. The obtained results are in accordance with their counterparts from the discrete-time case. Then we discuss the numerical approximation of the truncated Fourier transform based on non-equidistant high frequency data. In order to ensure convergence of the numerical approximation to the true value of the truncated Fourier transform a certain control on the maximal distance between observations and the number of observations is needed. We obtain both convergence to the continuous time quantity and asymptotic normality under a high-frequency infinite time horizon limit.<p>Key words and phrases: CARMA process, frequency domain, high-frequency data, Lévy process, trapezoidal rule.</span>
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VARIABLE SELECTION IN SPARSE REGRESSION WITH QUADRATIC MEASUREMENTS Jun Fan, Lingchen Kong, Liqun Wang and Naihua Xiu 1157-1178<span style='font-size=12pt;'><center>Abstract</center> Regularization methods for high-dimensional variable selection and estimation have been intensively studied in recent years and most of them are developed in the framework of linear regression models. However, in many problems, e.g., in compressive sensing, signal processing and imaging, the response variables are nonlinear functions of the unknown parameters. In this paper we introduce a so-called quadratic measurements regression model that extends the usual linear model. We study the 𝓁<sub>q</sub> regularized least squares method for variable selection and establish the weak oracle property of the corresponding estimator. Moreover, we derive a fixed point equation and use it to construct an efficient algorithm for numerical optimization. Numerical examples are given to demonstrate the finite sample performance of the proposed method and the efficiency of the algorithm. <p>Key words and phrases: 𝓁q-regularization, moderate deviation, optimization algorithm, sparsity, weak oracle property.</span>
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FAST ENVELOPE ALGORITHMS R. Dennis Cook and Xin Zhang 1179-1197<span style='font-size=12pt;'><center>Abstract</center> In this paper, we develop new fast algorithms for envelope estimation that are stable and can be used in contemporary complex envelope estimation problems. Under the sequential 1D envelope algorithm framework of Cook and Zhang (2016), we develop an envelope coordinate descent (ECD) algorithm that is shown to be much faster than the existing 1D algorithm without loss of accuracy. We also propose a novel class of envelope component screening (ECS) algorithms that serve as a screening step that can further significantly speed computation and that shows promise as precursor methodology when 𝓃 ≤ p . The ECD and ECS algorithms have both shown promising performance in extensive simulation studiesand a data analysis. <p>Key words and phrases: Envelope models, Grassmannian, reducing subspace.</span>
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FAST ENVELOPE ALGORITHMS R. Dennis Cook and Xin Zhang 1179-1197<span style='font-size=12pt;'><center>Abstract</center> In the statistical inference for long range dependent time series the shape of the limit distribution typically depends on unknown parameters. Therefore, we propose to use subsampling. We show the validity of subsampling for general statistics and long range dependent subordinated Gaussian processes that satisfy mild regularity conditions. We apply our method to a self-normalized change-point test statistic so that we can test for structural breaks in long range dependent time series without having to estimate nuisance parameters. The finite sample properties are investigated in a simulation study. We analyze three data sets and compare our results to the conclusions of other authors. <p>Key words and phrases: Change-point test, Gaussian processes, long range dependence, subsampling.</span>
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SUPERVISED LEARNING VIA THE "HUBNET" PROCEDURE Leying Guan, Zhou Fan and Robert Tibshirani 1225-1243<span style='font-size=12pt;'><center>Abstract</center> We propose a new method for supervised learning. The hubNet procedure fits a hub-based graphical model to the predictors, to estimate the amount of "connection" that each predictor has with other predictors. This yields a set of predictor weights that are then used in a regularized regression such as the lasso or elastic net. The resulting procedure is easy to implement, can often yield higher or competitive prediction accuracy with fewer features than the lasso, and can give insight into the underlying structure of the predictors. HubNet can be generalized seamlessly to supervised problems such as regularized logistic regression (and other GLMs), Cox's proportional hazards model, and nonlinear procedures such as random forests and boosting. We prove recovery results under a specialized model and illustrate the method on real and simulated data. <p>Key words and phrases: Adaptive lasso, graphical model, hubNet, unsupervised weights.</span>
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DYNAMIC NETWORK ANALYSIS WITH MISSING DATA: THEORY AND METHODS Zack W. Almquist and Carter T. Butts 1245-1264<span style='font-size=12pt;'><center>Abstract</center> Statistical methods for dynamic network analysis have advanced greatly in the past decade. This article extends current estimation methods for dynamic network logistic regression (DNR) models, a subfamily of the Temporal Exponential-family Random Graph Models, to network panel data which contain missing data in the edge and/or vertex sets. We begin by reviewing DNR inference in the complete data case. We then provide a missing data framework for DNR families akin to that of Little and Rubin (2002) or Gile and Handcock (2010a). We discuss several methods for dealing with missing data, including multiple imputation (MI). We consider the computational complexity of the MI methods in the DNR case and propose a scalable, design-based approach that exploits the simplifying assumptions of DNR. We dub this technique the "complete-case" method. Finally, we examine the performance of this method via a simulation study of induced missingness in two classic network data sets. <p>Key words and phrases: Dynamic network models, dynamic network models with missing data, dynamic network regression, ergm, exponential random graph models, logistic regression, missing data, temporal exponential random graph models, tergm.</span>
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SPARSE k-MEANS WITH 𝓁 ∞/𝓁 0 PENALTY FOR HIGH-DIMENSIONAL DATA CLUSTERING Xiangyu Chang, Yu Wang, Rongjian Li and Zongben Xu 1265-1284<span style='font-size=12pt;'><center>Abstract</center> One of the existing sparse clustering approaches, 𝓁<sub>1</sub>-k-means, maximizes the weighted between-cluster sum of squares subject to the 𝓁<sub>1</sub> penalty. In this paper, we propose a sparse clustering method based on an 𝓁<sub>∞</sub> / 𝓁<sub>0</sub> penalty, which we call 𝓁<sub>0</sub>-k-means. We design an efficient iterative algorithm for solving it. To compare the theoretical properties of 𝓁<sub>1</sub> and 𝓁<sub>0</sub>-k-means, we show that they can be explained explicitly from a thresholding perspective based on different thresholding functions. Moreover, 𝓁<sub>1</sub> and 𝓁<sub>0</sub>-k-means are proven to have a screening consistent property under Gaussian mixture models. Experiments on synthetic as well as real data justify the outperforming results of 𝓁<sub>0</sub> with respect to 𝓁<sub>1</sub>-k-means.<p>Key words and phrases: High-dimensional data clustering, screening property, sparse k-means.</span>
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AN IMPROVED MEASURE FOR LACK OF FIT IN TIME SERIES MODELS Thomas J. Fisher and Michael W. Robbins 1285-1305<span style='font-size=12pt;'><center>Abstract</center> The correlation structure of time series is of fundamental importance in diagnostic procedures. The squared autocorrelation function of the residuals of a fitted model is generally used as a measure of the goodness-of-fit; multivariate analogues are available for vector time series. As an alternative, we propose a logarithmic transformation of the determinant of a constructed Toeplitz matrix containing the typical measure of correlation. We show that the proposed measure is asymptotically more powerful than the typical measure of correlation (when used with or without the Ljung-Box correction) in the detection of a variety of residual dependence structures. The proposed method is shown to have utility when applied in conjunction with a host of methods used to diagnose the fit of strong and weak autoregressive moving average models and generalized autoregressive conditional heteroskedastic models. A simulation study demonstrates the effectiveness of the proposed method and illustrates its improvement over the existent procedures. <p>Key words and phrases: Autocorrelation, GARCH, goodness-of-fit, portmanteau, vector ARMA.</span>