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Statistica Sinica 21 (2011), 949-971



Yanyuan Ma and Guosheng Yin

Texas A& M University and The University of Hong Kong

Abstract: We study censored quantile regression with covariates measured with errors. We propose a composite quantile objective function based on inverse censoring-probability weighting, and an averaging estimator to improve estimation efficiency. Our procedure can eliminate the bias in the naive estimator that is obtained by treating mismeasured covariates as error-free. Using a combination of martingale and quantile regression techniques, we show that the proposed estimators for the regression coefficients are consistent and asymptotically normal. We conducted simulation studies to examine the finite-sample properties of the new method, and demonstrated efficiency gain of the averaging estimator over the single quantile regression estimator. For illustration, we applied our model to a lung cancer study.

Key words and phrases: Averaging estimation, bootstrap, errors-in-variables problem, regression quantiles, semiparametric method, survival data.

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