Joint approximation of processes based on spacings and order statistics

Philippe Barbe

Stochastic Processes and their Applications, 1994, vol. 53, issue 2, 339-349

Abstract: Let [omega]1, [omega]2, ... be a sequence of i.i.d. r.v. with E[omega]1 [not equal to] 0 and Var [omega]i = 1. Under some weak conditions on the distribution of the [omega]i's, we give a joint approximation of the empirical process corresponding to and the empirical process corresponding to the spacings empirical distribution function . We apply this result to show that a large class of statistics based on spacings and order statistics of a uniform sample are asymptotically independent, leading to some improved goodness of fit tests.

Keywords: Renewal; spacing; process; Renewal; empirical; distribution; function (search for similar items in EconPapers)
Date: 1994
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Citations: View citations in EconPapers (3)

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