Almost Sure Behaviour of $U$-Statistics and Von Mises' Differentiable Statistical Functions
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.
Permanent link to this document: http://projecteuclid.org/euclid.aos/1176342675
Digital Object Identifier: doi:10.1214/aos/1176342675
Mathematical Reviews number (MathSciNet): MR362634
Zentralblatt MATH identifier: 0276.60009