Approximations for weighted bootstrap processes with an application

Let [beta]n(t) denote the weighted (smooth) bootstrap process of an empirical process. We show that the order of the best Gaussian approximation for [beta]n(t) is n-1/2 log n and we construct a sequence of approximating Brownian bridges achieving this rate. We also obtain an approximation for [beta]n(t) using a suitably chosen Kiefer process. The result is applied to detect a possible change in the distribution of independent observations.

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Year of publication:	2000
Authors:	Horváth, Lajos ; Kokoszka, Piotr ; Steinebach, Josef
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 48.2000, 1, p. 59-70
Publisher:	Elsevier
Keywords:	Weighted bootstrap Erdös-Rényi law Brownian bridge Best approximation Change-point detection

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005254541