$U$-Statistic Processes: A Martingale Approach
نویسندگان
چکیده
منابع مشابه
Moment Inequalities for Supremum of Empirical Processes of U-Statistic Structure and Application to Density Estimation
We derive moment inequalities for the supremum of empirical processes of U-Statistic structure and give application to kernel type density estimation and estimation of the distribution function for functions of observations.
متن کاملAsymptotic analysis for bifurcating autoregressive processes via a martingale approach
We study the asymptotic behavior of the least squares estimators of the unknown parameters of general pth-order bifurcating autoregressive processes. Under very weak assumptions on the driven noise of the process, namely conditional pair-wise independence and suitable moment conditions, we establish the almost sure convergence of our estimators together with the quadratic strong law and the cen...
متن کاملU-statistic with side information
In this paper we study U-statistics with side information incorporated using the method of empirical likelihood. Some basic properties of the proposed statistics are investigated. We find that by implementing the side information properly, the proposed U-statistics can have smaller asymptotic variance than the existing U-statistics in the literature. The proposed U-statistics can achieve asympt...
متن کاملMartingale Property of Empirical Processes ¤
It is shown that for a large collection of almost independent martingales in a suitable framework, the martingale property is preserved on the empirical processes almost surely. Under the assumptions of almost independence and essentially identical finite dimensional distributions, it is proven that a large collection of stochastic processes are martingales essentially if and only if so are the...
متن کاملOn Local U -statistic Processes and the Estimation of Densities of Functions of Several Sample Variables
A notion of local U -statistic process is introduced and central limit theorems in various norms are obtained for it. This involves the development of several inequalities for U -processes that may be useful in other contexts. This local U -statistic process is based on an estimator of the density of a function of several sample variables proposed by Frees [J. Amer. Statist. Assoc. 89 (1994) 51...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Probability
سال: 1994
ISSN: 0091-1798
DOI: 10.1214/aop/1176988480