Qunying Wu

A complete convergence theorem for weighted sums of arrays of rowwise negatively dependent random variables

In this article, applying moment inequality of negatively dependent (ND) random variables which obtained by Asadian et al., the complete convergence theorem for weighted sums of arrays of rowwise ND random variables is discussed. As a result, the complete convergence theorem for ND arrays of random variables is extended. Our results generalize and improve those on complete convergence theorem previously obtained by Hu et al., Ahmed et al, Volodin, and Sung from the independent and identically distributed case to ND sequences.Mathematical Subject Classification: 62F12.

A Strong Limit Theorem for Weighted Sums of Sequences of Negatively Dependent Random Variables

Applying the moment inequality of negatively dependent random variables which was obtained by Asadian et al. (2006), the strong limit theorem for weighted sums of sequences of negatively dependent random variables is discussed. As a result, the strong limit theorem for negatively dependent sequences of random variables is extended. Our results extend and improve the corresponding results of Bai and Cheng (2000) from the i.i.d. case to ND sequences.

Complete Convergence for Negatively Dependent Sequences of Random Variables

We study the complete convergence for negatively dependent sequences of random variables. As a result, we extend some complete convergence theorems for independent random variables to the case of negatively dependent random variables without necessarily imposing any extra conditions.

The Strong Consistency of M Estimator in a Linear Model for Negatively Dependent Random Samples

The strong consistency of M estimators of the regression parameters in linear models for negatively dependent random errors under some mild conditions is established, which is an essential improvement on the relevant results in the literature on the moment conditions and dependent errors. Especially, Theorems 1 and 2 of Wu (2006) are not only extended to the case of negatively dependent random errors, but also are improved essentially on the moment conditions.

THE STRONG LAW OF LARGE NUMBERS FOR PAIRWISE NQD RANDOM VARIABLES

In this paper, the almost sure convergence for pairwise negatively quadrant dependent random variables is studied. The strong law of large numbers for pairwise negatively quadrant dependent random variables is obtained. Our results generalize and improve those on almost sure convergence theorems previously obtained by Marcinkiewicz (1937), Jamison (1965), Matula (1992) and Wu (2001) from the independent identically distributed (i.i.d.) case to pairwise NQD sequences.

A note on the almost sure limit theorem for self-normalized partial sums of random variables in the domain of attraction of the normal law

Let X, X1, X2,... be a sequence of independent and identically distributed random variables in the domain of attraction of a normal distribution. A universal result in almost sure limit theorem for the self-normalized partial sums Sn/Vnis established, where Sn=∑i=1nXi,Vn2=∑i=1nXi2.Mathematical Scientific Classification: 60F15.

Sufficient and Necessary Conditions of Complete Convergence for Weighted Sums of PNQD Random Variables

The complete convergence for pairwise negative quadrant dependent (PNQD) random variables is studied. So far there has not been the general moment inequality for PNQD sequence, and therefore the study of the limit theory for PNQD sequence is very difficult and challenging. We establish a collection that contains relationship to overcome the difficulties that there is no general moment inequality. Sufficient and necessary conditions of complete convergence for weighted sums of PNQD random variables are obtained. Our results generalize and improve those on complete convergence theorems previously obtained by Baum and Katz (1965) and Wu (2002).

Chover’s law of the iterated logarithm for negatively associated sequences

Consider a sequence of negatively associated and identically distributed random variables with the underlying distribution in the domain of attraction of a stable distribution with an exponent in (0, 2). A Chover’s law of the iterated logarithm is established for negatively associated random variables. Our results generalize and improve those on Chover’s law of the iterated logarithm (LIL) type behavior previously obtained by Mikosch (1984), Vasudeva (1984), and Qi and Cheng (1996) from the i.i.d. case to NA sequences.

STRONG CONSISTENCY OF M ESTIMATOR IN LINEAR MODEL FOR NEGATIVELY ASSOCIATED SAMPLES

This paper discusses the strong consistency of M estimator of regression parameter in linear model for negatively associated samples. As a result, the author extends Theorem 1 and Theorem 2 of Shanchao YANG (2002) to the NA errors without necessarily imposing any extra condition.

An improved result in almost sure central limit theorem for self-normalized products of partial sums

Let X,X1,X2,… be a sequence of independent and identically distributed random variables in the domain of attraction of the normal law. A universal result in an almost sure limit theorem for the self-normalized products of partial sums is established.MSC:60F15.