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

Stefan Ralescu and Madan L. Puri

Journal of Multivariate Analysis, 1984, vol. 14, issue 2, 231-247

Abstract: 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 .

Keywords: Berry-Esseen; rates; law; of; iterated; logarithm; invariance; principle; Gateaux-differential (search for similar items in EconPapers)
Date: 1984
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