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Convergence of integrals of uniform empirical and quantile processes

We find a necessary and sufficient condition for the weak convergence of the uniform empirical and quantile processes to a Brownian bridge in weighted Lp-distances. Under the same condition, weighted Lp-functionals of the uniform empirical and quantile processes converge in distribution to the corresponding functionals of a Brownian bridge. We also prove some dichotomy theorems for integrals of stochastic processes.
Year of publication:
1993
Authors: Csörgo, Miklós ; Horváth, Lajos ; Shao, Qi-Man
Published in:
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 45.1993, 2, p. 283-294
Publisher: Elsevier
Keywords: empirical and quantile processes stochastic integrals dichotomy Lp-distance Brownian bridge
Type of publication: Article
Source:
Persistent link: https://www.econbiz.de/10008875330
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