A maximal moment inequality for partial sums of the [alpha]-mixing random variable sequence is established. The inequality uses some moment summations as upper bound. To show the applications of the inequality, we discuss the convergence for [alpha]-mixing sequences, which improves some known...

Consider the wavelet estimator of a nonparametric fixed design regression function when errors are strictly stationary and associated random variables. We establish pointwise weak consistency and uniformly asymptotic normality of wavelet estimator of regression function. We give rates of...

A general method to prove the strong law of large numbers is given by using the maximal tail probability. As a result the convergence rate of Sn/n for both positively associated sequences and negatively associated sequences is for any [delta]1. This result closes to the optimal achievable...

In this paper, we establish an inequality of the characteristic functions for strongly mixing random vectors, by which, an upper bound is provided for the supremum of the absolute value of the difference of two multivariate probability density functions based on strongly mixing random vectors....