On the Glivenko-Cantelli theorem for generalized empirical processes based on strong mixing sequences

Y. S. Rama Krishnaiah

Statistics & Probability Letters, 1990, vol. 10, issue 5, 439-447

Abstract: Given \s{Xi, i [greater-or-equal, slanted] 1\s} as non-stationary strong mixing (n.s.s.m.) sequence of random variables (r.v.'s) let, for 1 [less-than-or-equals, slant] i [less-than-or-equals, slant] n and some [gamma] [epsilon] [0, 1], F1(x)=[gamma]P(Xi 0, and a rate for the almost sure convergence of Dn are obtained under strong mixing. These results generalize those of Singh (1975) for the independent and non-identically distributed sequence of r.v.'s to the case of strong mixing.

Keywords: Generalized; empirical; processes; strong; mixing; almost; sure; convergence (search for similar items in EconPapers)
Date: 1990
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