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

Pranab Kumar Sen
Source: Ann. Statist. Volume 2, Number 2 (1974), 387-395.

#### 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.

First Page:
Primary Subjects: 60B10
Secondary Subjects: 60F15, 62E20
Full-text: Open access