On Self‐Normalization for Censored Dependent Data

Abstract

This article is concerned with confidence interval construction for functionals of the survival distribution for censored dependent data. We adopt the recently developed self‐normalization approach (Shao, 2010), which does not involve consistent estimation of the asymptotic variance, as implicitly used in the blockwise empirical likelihood approach of El Ghouch et al. (2011). We also provide a rigorous asymptotic theory to derive the limiting distribution of the self‐normalized quantity for a wide range of parameters. Additionally, finite‐sample properties of the self‐normalization‐based intervals are carefully examined, and a comparison with the empirical likelihood‐based counterparts is made.

Keywords: Censored data, dependence, empirical likelihood, quantile, self‐normalization, survival analysis