Power-Transformed Linear Quantile Regression With Censored Data

We propose a class of power-transformed linear quantile regression models for survival data subject to random censoring. The estimation procedure follows two sequential steps. First, for a given transformation parameter, we can easily obtain the estimates for the regression coefficients by minimizing a well-defined convex objective function. Second, we can estimate the transformation parameter based on a model discrepancy measure by constructing cumulative sum processes. We show that both the regression and transformation parameter estimates are strongly consistent and asymptotically normal. The variance–covariance matrix depends on the unknown density function of the error term, so we estimate the variance by the usual bootstrap approach. We examine the performance of the proposed method for finite sample sizes through simulation studies and illustrate it with a real data example.

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