On the Estimation of Conditional Tail Index and Extreme Quantiles under Random Censoring

Abstract

In the area of Statistics of Extremes, the main assumption on any set of univariate data is to regard them as a complete sample of independent and identically distributed observations from an unknown distribution function, F. However, in many real life applications such as survival analysis, observations are usually subject to random censoring and may be influenced by an underlying covariate information. In such case, the classical extreme value theory needs some adjustment to take into account the presence of censoring and covariates. In this presentation, we propose estimators of the conditional tail index and conditional extreme quantiles for heavy-tailed distributions in the presence of random censoring and covariate information. We compare the proposed estimators with the existing estimators in the literature in a large scale simulation study. The results show improvement in bias and median absolute deviation over the existing estimators of the conditional tail index and conditional extreme quantiles.