Bernstein-Type Inequality for Widely Dependent Sequence and Its Application to Nonparametric Regression Models

We present the Bernstein-type inequality for widely dependent random variables. By using the Bernstein-type inequality and the truncated method, we further study the strong consistency of estimator of fixed design regression model under widely dependent random variables, which generalizes the corresponding one of independent random variables. As an application, the strong consistency for the nearest neighbor estimator is obtained

On Complete Convergence for Weighted Sums of ρ

We prove the strong law of large numbers for weighted sums ∑i=1n‍aniXi, which generalizes and improves the corresponding one for independent and identically distributed random variables and φ-mixing random variables. In addition, we present some results on complete convergence for weighted sums of ρ*-mixing random variables under some suitable conditions, which generalize the corresponding ones for independent random variables

Complete Convergence of the Maximum Partial Sums for Arrays of Rowwise of AANA Random Variables

The limiting behavior of the maximum partial sums | is investigated, and some new results are obtained, where { , ≥ 1, ≥ 1} is an array of rowwise AANA random variables and { , ≥ 1} is a sequence of positive real numbers. As an application, the Chung-type strong law of large numbers for arrays of rowwise AANA random variables is obtained. The results extend and improve the corresponding ones of Hu and Taylor (1997) for arrays of rowwise independent random variables

A Note on the Inverse Moments for Nonnegative -Mixing Random Variables

Wu et al. (2009) studied the asymptotic approximation of inverse moments for nonnegative independent random variables. Shen et al. (2011) extended the result of Wu et al. (2009) to the case of -mixing random variables. In the paper, we will further study the asymptotic approximation of inverse moments for nonnegative -mixing random variables, which improves the corresponding results of Wu et al. (2009), Wang et al. (2010), and Shen et al. (2011) under the case of identical distribution

On Strong Convergence for Weighted Sums of a Class of Random Variables

Let {Xn,n≥1} be a sequence of random variables satisfying the Rosenthal-type maximal inequality. Complete convergence is studied for linear statistics that are weighted sums of identically distributed random variables under a suitable moment condition. As an application, the Marcinkiewicz-Zygmund-type strong law of large numbers is obtained. Our result generalizes the corresponding one of Zhou et al. (2011) and improves the corresponding one of Wang et al. (2011, 2012)

Some strong limit theorems for arrays of rowwise negatively orthant-dependent random variables

Abstract In this article, the strong limit theorems for arrays of rowwise negatively orthant-dependent random variables are studied. Some sufficient conditions for strong law of large numbers for an array of rowwise negatively orthant-dependent random variables without assumptions of identical distribution and stochastic domination are presented. As an application, the Chung-type strong law of large numbers for arrays of rowwise negatively orthant-dependent random variables is obtained. MR(2000) Subject Classification: 60F15</p

Strong and Weak Convergence for Asymptotically Almost Negatively Associated Random Variables

The strong law of large numbers for sequences of asymptotically almost negatively associated (AANA, in short) random variables is obtained, which generalizes and improves the corresponding one of Bai and Cheng (2000) for independent and identically distributed random variables to the case of AANA random variables. In addition, the Feller-type weak law of large number for sequences of AANA random variables is obtained, which generalizes the corresponding one of Feller (1946) for independent and identically distributed random variables

A Note on the Strong Law of Large Numbers for Arrays of Rowwise ρ˜-Mixing Random Variables

Let {Xni,i≥1,n≥1} be an array of rowwise ρ˜-mixing random variables. Some strong law of large numbers for arrays of rowwise ρ˜-mixing random variables is studied under some simple and weak conditions