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Convergence of integrals of uniform empirical and quantile processes

Miklós Csörgo, Lajos Horvath and Qi-Man Shao

Stochastic Processes and their Applications, 1993, vol. 45, issue 2, 283-294

Abstract: 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.

Keywords: empirical; and; quantile; processes; stochastic; integrals; dichotomy; Lp-distance; Brownian; bridge (search for similar items in EconPapers)
Date: 1993
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Handle: RePEc:eee:spapps:v:45:y:1993:i:2:p:283-294