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December 1995 Sequential confidence bands for densities
Yi Xu, Adam T. Martinsek
Ann. Statist. 23(6): 2218-2240 (December 1995). DOI: 10.1214/aos/1034713654


This paper proposes a fully sequential procedure for constructing a fixed-width confidence band for an unknown density on a finite interval and shows 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. 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.


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Yi Xu. Adam T. Martinsek. "Sequential confidence bands for densities." Ann. Statist. 23 (6) 2218 - 2240, December 1995.


Published: December 1995
First available in Project Euclid: 15 October 2002

zbMATH: 0897.62093
MathSciNet: MR1389872
Digital Object Identifier: 10.1214/aos/1034713654

Primary: 62L12
Secondary: 62G07, 62G20

Rights: Copyright © 1995 Institute of Mathematical Statistics


Vol.23 • No. 6 • December 1995
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