The Annals of Statistics

Almost Sure Behaviour of $U$-Statistics and Von Mises' Differentiable Statistical Functions

Pranab Kumar Sen

Full-text: Open access

Abstract

For $U$-Statistics and von Mises' differentiable statistical functions, when the regular functional is stationary of order zero, almost sure convergence to appropriate Wiener processes is studied. A second almost sure invariance principle, particularly useful in the context of the law of iterated logarithm and the probability of moderate deviations, is also established.

Article information

Source
Ann. Statist., Volume 2, Number 2 (1974), 387-395.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176342675

Digital Object Identifier
doi:10.1214/aos/1176342675

Mathematical Reviews number (MathSciNet)
MR362634

Zentralblatt MATH identifier
0276.60009

JSTOR
links.jstor.org

Subjects
Primary: 60B10: Convergence of probability measures
Secondary: 60F15: Strong theorems 62E20: Asymptotic distribution theory

Keywords
Almost sure convergence invariance principle Wiener process $U$-statistics von Mises' functionals law of iterated logarithm and probability of moderate deviations

Citation

Sen, Pranab Kumar. Almost Sure Behaviour of $U$-Statistics and Von Mises' Differentiable Statistical Functions. Ann. Statist. 2 (1974), no. 2, 387--395. doi:10.1214/aos/1176342675. https://projecteuclid.org/euclid.aos/1176342675


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