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Abstract:
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Quantile regression has emerged as a powerful tool for survival analysis with censored data. In this article, we propose an efficient estimator for the coefficient in quantile regression with censored data using the envelope model. First introduced in Cook et al. (2010), the envelope model uses dimension reduction techniques to identify material and immaterial components in the data, and forms the estimator of the regression coefficient based only on the material component, thus reducing the variability of the estimation. We will derive asymptotic properties of the proposed estimator and demonstrate its efficiency gains as compared to the traditional estimator for quantile regression with censored data. Recent advances in algorithms for the envelope model allow for efficient implementation of the proposed method. The strength of our proposed method is demonstrated via simulation studies.
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