, Volume 21, Issue 3, pp 672-686
Date: 23 Oct 2007

Weak Convergence of Vervaat and Vervaat Error Processes of Long-Range Dependent Sequences

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Abstract

Following Csörgő, Szyszkowicz and Wang (Ann. Stat. 34, 1013–1044, 2006) we consider a long range dependent linear sequence. We prove weak convergence of the uniform Vervaat and the uniform Vervaat error processes, extending their results to distributions with unbounded support and removing normality assumption.

Research supported in part by NSERC Canada Discovery Grants of Miklós Csörgő, Donald Dawson and Barbara Szyszkowicz at Carleton University.