On the Distance Between Smoothed Empirical and Quantile Processes

The Annals of Statistics · 1995 · Volume 23 · Issue 1

Abstract

We consider Bahadur-Kiefer representations for smoothed quantile processes. We prove that the asymptotics of the distance between smoothed empirical and quantile processes can be completely different from that of the unsmoothed ones. We obtain a complete characterization of the possible limits.

Keywords

60F05; 62G30; Bahadur-Kiefer representation; Brownian bridge; empirical process; Kernel-smoothing; quantile process;

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