doi:http://dx.doi.org/10.5705/ss.2010.109
Abstract: In this paper we develop model checking techniques for assessing functional form specifications of covariates in censored linear regression models. These procedures are based on a censored data analog to taking cumulative sums of ``robust'' residuals over the space of the covariate under investigation. These cumulative sums are formed by integrating certain Kaplan-Meier estimators and may be viewed as ``robust'' censored data analogs to the processes considered by Lin, Wei, and Ying (2002). The null distributions of the stochastic processes can be approximated by the distributions of certain zero-mean Gaussian processes whose realizations can be generated by computer simulation. Each observed process can then be graphically compared with a few realizations from the Gaussian process. We also develop formal test statistics for numerical comparison. Such comparisons enable one to assess objectively whether an apparent trend seen in a residual plot reflects model misspecification or natural variation. We illustrate the methods with a well-known dataset. In addition, we examine the finite sample performance of the proposed test statistics in simulation experiments. In them, the proposed test statistics have good power for detecting misspecification while at the same time controlling the size of the test.
Key words and phrases: Censored linear regression, goodness-of-fit, partial linear model, partial residual, quantile regression, resampling method, rank estimation.