A Remark on Convergence in Distribution of $U$-Statistics

A Remark on Convergence in Distribution of U-statistics

It is proved that, for h measurable and symmetric in its arguments and Xi i.i.d., if the sequence {n−m2 ∑ i1,...,im≤n ij 6=ik if j 6=k h(Xi1 ,...,Xim )}n=1, is stochastically bounded, then Eh2<∞ and Eh(X1,x2,...,xm)=0 a.s.

Weak Convergence of Generalized U - Statistics

A Remark on the Gromov Convergence Theorem

In [3] M. Gromov introduced the concept of convergence of Riemannian manifolds and he proved the convergence theorem. Since that time the theorem has been developed in detail (see [5], [7], [2]), and we know that it contains some interesting applications. Nevertheless there seems to be an inadequate way of applying the convergence theorem. The purpose of this paper is to present an example whic...

Asymptotics for the Moment Convergence of U-Statistics in LIL

On Performance of Reconstructed Middle Order Statistics in Exponential Distribution

&nbsp;In a number of life-testing experiments, there exist situations where the monitoring breaks down for a temporary period of time. In such cases, some parts of the ordered observations, for example the middle ones, are censored and the only outcomes available for analysis consist of the lower and upper order statistics. Therefore, the experimenter may not gain the complete information on fa...