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https://hdl.handle.net/2142/23054
Description
Title
Sequential confidence bands for densities
Author(s)
Xu, Yi
Issue Date
1995
Doctoral Committee Chair(s)
Martinsek, Adam T.
Department of Study
Statistics
Discipline
Statistics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Statistics
Language
eng
Abstract
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.
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