Statistics and Its Interface

Volume 10 (2017)

Number 2

Power-transformed linear quantile regression estimation for censored competing risks data

Pages: 239 – 254

DOI: http://dx.doi.org/10.4310/SII.2017.v10.n2.a8

Authors

Caiyun Fan (School of Statistics and Information, Shanghai University of International Business and Economics, Shanghai, China)

Feipeng Zhang (School of Finance and Statistics, Hunan University, Changsha, China)

Yong Zhou (School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai, China; and Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China)

Abstract

This paper considers a power-transformed linear quantile regression model for censored competing risks data, based on conditional quantiles defined by using the cumulative incidence function. We propose a two-stage estimating procedure for the regression coefficients and the transformation parameter. In the first step, for a given transformation parameter, we develop an unbiased monotone estimating equation for regression parameters in the quantile model, which can be solved by minimizing a $L_1$ type convex objective function. In the second step, the transformation parameter can be estimated by constructing the cumulative sum processes. The consistency and asymptotic normality of the regression parameters and transformation parameter are derived. The finite-sample performances of the proposed approach are illustrated by simulation studies and an application to the follicular type lymphoma data set.

Keywords

Box-Cox transformation, censored data, competing risks, quantile regression

2010 Mathematics Subject Classification

Primary 62G08, 62N01, 62N02, 62P10. Secondary 60G07, 62G07, 62G20.

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