Sequential confidence bands for densities

We propose a fully sequential procedure for constructing a fixed width confidence band for an unknown density on a finite interval and show the procedure has the desired coverage probability asymptotically as the width of the band approaches zero. The procedure is based on a result of Bickel and Rosenblatt (1973, Ann. Statist. 1, 1071-1095). Its implementation in the sequential setting cannot be obtained using Anscombe's theorem, because the normalized maximal deviations between the kernel estimate and the true density are not uniformly continuous in probability (u.c.i.p.). Instead, we obtain a slightly weaker version of the u.c.i.p. property and a correspondingly stronger convergence property of the stopping rule. These together yield the desired results. We also present some simulation results and applications of the basic method to stopping rules of interest. Similar result is also obtained for censored data case.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Statistics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Xu, Yi

Contributors dc:contributor

• Martinsek, Adam T.

• Statistics

Statement dc:rights

• Copyright 1995 Xu, Yi

Language dc:language

eng

Identifier

AAI9543778
(UMI)AAI9543778

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/23054