Nonparametric Estimations for Quantile Residual Life Function with Left Truncated and Right Censored Data

Abstract

The use of residual life function to make prediction is widely used in many fields, such as reliability, medical studies, actuarial science and business. This talk will give brief introduction to nonparametric estimations for quantile residual life function with left truncated and right censored data and will be divided into three parts. ????? The first part includes three types of confidence intervals for median residual lifetime in one sample problem. Comparisons of those confidence intervals will be displayed with numerical simulations. The second part not only extends the estimation methods to two sample problem but also introduces a confidence interval with simpler computation and corrected confidence coefficient. The final part introduces the literature history, concept and estimation methods of confidence bands for quantile residual life function. The martingale technique is used to develop the large sample theory of proposed band. In addition, the data set from the Survey of Health and Living Status of the Middle Aged and Elderly in Taiwan will be used to demonstrate our methods. Keywords: quantile residual life function, confidence band, left truncated and right censored data, martingale.