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On Berry-Esséen rates, a law of the iterated logarithm and an invariance principle for the proportion of the sample below the sample mean

Let Fn(x) be the empirical distribution function based on n independent random variables X1,...,Xn from a common distribution function F(x), and let be the sample mean. We derive the rate of convergence of to normality (for the regular as well as nonregular cases), a law of iterated logarithm, and an invariance principle for .
Year of publication:
1984
Authors: Ralescu, Stefan ; Puri, Madan L.
Published in:
Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 14.1984, 2, p. 231-247
Publisher: Elsevier
Keywords: Berry-Esseen rates law of iterated logarithm invariance principle Gateaux-differential
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Type of publication: Article
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Persistent link: https://www.econbiz.de/10005106941
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