Non-uniform Berry–Esseen Bounds for Weighted U-Statistics and Generalized L-Statistics

On weighted U-statistics for stationary processes

A weighted U -statistic based on a random sample X1, . . . , Xn has the form Un = ∑ 1≤i,j≤n wi−jK(Xi, Xj) where K is fixed symmetric measurable function and the wi are symmetric weights. A large class of statistics can be expressed as weighted U -statistics or variations thereof. This paper establishes the asymptotic normality of Un when the sample observations come from a non-linear time serie...

Strong Laws for L- and U-statistics

Strong laws of large numbers are given for L-statistics (linear com­ binations of order statistics) and for U -statistics (averages of kernels of ran­ dom samples) for ergodic stationary processes, extending classical theorems of Hoeffding and of Helmers for iid sequences. Examples are given to show that strong and even weak convergence may fail if the given sufficient conditions are not satisf...

Uniform and Non-uniform Bounds in Normal Approximation for Nonlinear Statistics

Let T be a general sampling statistic that can be written as a linear statistic plus an error term. Uniform and non-uniform Berry-Esseen type bounds for T are obtained. The bounds are best possible for many known statistics. Applications to U-statistic, multi-sample U-statistic, L-statistic, random sums, and functions of non-linear statistics are discussed.

Weak Convergence of Generalized U - Statistics

Inferences for Extended Generalized Exponential Distribution based on Order Statistics

‎Recently‎, ‎a new distribution‎, ‎named as extended generalized exponential distribution‎, ‎has been introduced by Kundu and Gupta (2011). ‎In this paper‎, ‎we consider the extended generalized exponential distribution with known shape parameters α and β. ‎At first‎, ‎the exact expressions for marginal and product moments of o...