Nonparametric inference strategies for the quantile functions under left truncation and right censoring

Abstract

This paper addresses the problem of estimating the quantile function in a multiple-sample set up when the data are left-truncated and right-censored (LTRC). Assuming an uncertain prior non-sample information on the value of the quantile, we propose improved estimators based on Stein-type shrinkage estimators. A test statistic is also proposed to define improved estimators for the quantile function. The asymptotic bias and risk of the estimators are derived and compared with the benchmark estimator analytically. For several choices of parameters, a Monte Carlo simulation experiment is conducted to appraise the risk reduction of the proposed estimators at different levels of censoring and truncation. We demonstrate that the proposed estimators have superior performance in terms of risk reduction over the benchmark estimator.