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

DOI10.1016/0047-259X(84)90008-3zbMath0534.60021MaRDI QIDQ790516

Madan Lal Puri, Stefan S. Ralescu

Publication date: 1984

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

zbMATH Keywords

invariance principlelaw of iterated logarithmempirical distribution functionBerry-Esséen ratesGâteaux-differential

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Central limit and other weak theorems (60F05) Strong limit theorems (60F15) Functional limit theorems; invariance principles (60F17)

Related Items (4)

Central limit theorem for perturbed empirical distribution functions evaluated at a random point ⋮ The asymptotic law of the local oscillation modulus of the empirical process ⋮ Law of the iterated logarithm for perturbed empirical distribution functions evaluated at a random point for nonstationary random variables ⋮ Empirical process of long-range dependent sequences when parameters are estimated

Cites Work

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• Approximation Theorems of Mathematical Statistics
• Tests for symmetry
• Some Comments on the Asymptotic Probability Laws of Sample Quantiles
• The Sample Mean Among the Moderate Order Statistics
• A Note on Quantiles in Large Samples
• On Bahadur's Representation of Sample Quantiles
• On the Sign Test for Symmetry
• A New Proof of the Bahadur Representation of Quantiles and an Application

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