Estimation Of High Conditional Quantiles For Censored Data

The estimation of high conditional quantiles is of great importance in numerous disciplines. Quantile regression provides a convenient and natural way to model the effects of covariates at dierent tails of the response distribution. However, conventional quantile regression estimation at very high or low tails is ofen unstable and sufer from high variability especially for heavy-tailed distributions because of data sparsity. Moreover, censored data will make the situation worse. In this paper, we consider the estimation problem of high conditional quantiles under random censoring. We develop two new estimation methods by combining conventional quantile regression of censored data and extreme value theory. Numerical results of our methods on simulated data and a real data are given to demonstrate the merits of the proposed method. This paper can be summarized brifly as follows:In the first chapter, we introduce the related theory and model.In the second chapter, we introduce estimation of high conditional quantiles of complete data.In the third chapter, we develop two new estimation methods by combining conventional quantile regression of censored data and extreme value theory.In the fourth chapter, we show the numerical simulation results to analyze the robustness of the method.In the fifth chapter, we provide the proof of asymptotic property in the third chapter.