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March, 1974 Almost Sure Behaviour of $U$-Statistics and Von Mises' Differentiable Statistical Functions
Pranab Kumar Sen
Ann. Statist. 2(2): 387-395 (March, 1974). DOI: 10.1214/aos/1176342675

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.

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Pranab Kumar Sen. "Almost Sure Behaviour of $U$-Statistics and Von Mises' Differentiable Statistical Functions." Ann. Statist. 2 (2) 387 - 395, March, 1974. https://doi.org/10.1214/aos/1176342675

Information

Published: March, 1974
First available in Project Euclid: 12 April 2007

zbMATH: 0276.60009
MathSciNet: MR362634
Digital Object Identifier: 10.1214/aos/1176342675

Subjects:
Primary: 60B10
Secondary: 60F15, 62E20

Rights: Copyright © 1974 Institute of Mathematical Statistics

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Vol.2 • No. 2 • March, 1974
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