Almost sure limit theorems for U-statistics
نویسندگان
چکیده
We relax the moment conditions from a result in almost sure limit theory for U-statistics due to Berkes and Csaki (2001). We extend this result to the case of convergence to stable laws and also prove a functional version.
منابع مشابه
Almost sure central limit theorems on the Wiener space
In this paper, we study almost sure central limit theorems for sequences of functionals of general Gaussian elds. We apply our result to non-linear functions of stationary Gaussian sequences. We obtain almost sure central limit theorems for these non-linear functions when they converge in law to a normal distribution.
متن کاملSome limit theorems for ratios of order statistics from uniform random variables
In this paper, we study the ratios of order statistics based on samples drawn from uniform distribution and establish some limit properties such as the almost sure central limit theorem, the large deviation principle, the Marcinkiewicz-Zygmund law of large numbers and complete convergence.
متن کاملIntegral analogues of almost sure limit theorems
An integral analogue of the general almost sure limit theorem is presented. In the theorem, instead of a sequence of random elements, a continuous time random process is involved, moreover, instead of the logarithmical average, the integral of delta-measures is considered. Then the general theorem is applied to obtain almost sure versions of limit theorems for semistable and max-semistable proc...
متن کاملAlmost sure limit theorems for the maximum of stationary Gaussian sequences
We prove an almost sure limit theorem for the maxima of stationary Gaussian sequences with covariance rn under the condition rn log n (log log n)1+ε = O(1).
متن کاملThe Almost Sure Local Central Limit Theorem for the Negatively Associated Sequences
In this paper, the almost sure central limit theorem is established for sequences of negatively associated random variables: lim n→∞ (1/ log n)∑n k=1 (I(a k ≤ S k < b k )/k)P(a k ≤ S k < b k ) = 1, almost surely. This is the local almost sure central limit theorem for negatively associated sequences similar to results by Csáki et al. (1993). The results extend those on almost sure local central...
متن کامل