Shuhe Hu

Complete consistency for the estimator of nonparametric regression models based on extended negatively dependent errors

In this paper, we provide some exponential inequalities for extended negatively dependent (END) random variables. By using these exponential inequalities and the truncated method, we investigate the complete consistency for the estimator of nonparametric regression model based on END errors. As an application, the complete consistency for the nearest neighbour estimator is obtained.

Complete Convergence for Weighted Sums and Arrays of Rowwise Extended Negatively Dependent Random Variables

In this article, we study the complete convergence for weighted sums of extended negatively dependent random variables and row sums of arrays of rowwise extended negatively dependent random variables. We apply two methods to prove the results: the first of is based on exponential bounds and second is based on the generalization of the classical moment inequality for extended negatively dependent random variables.

The consistency for estimator of nonparametric regression model based on NOD errors

By using some inequalities for NOD random variables, we give its application to investigate the nonparametric regression model based on these errors. Some consistency results for the estimator of g(x) are presented, including the mean convergence, uniform convergence, almost sure convergence and convergence rate. We generalize some related results and as an example of designed assumptions for weight functions, we give the nearest neighbor weights.AMS Mathematical Subject Classification 2000: 62G05; 62G08.

On complete convergence for arrays of rowwise weakly dependent random variables

Abstract Some sufficient conditions for complete convergence for arrays of rowwise ρ -mixing random variables are presented without the assumption of identical distributions. As an application, the Marcinkiewicz–Zygmund type strong law of large numbers for weighted sums of ρ -mixing random variables is obtained.

On Complete Convergence for an Extended Negatively Dependent Sequence

In this article, the Rosenthal-type maximal inequality for extended negatively dependent (END) sequence is provided. By using the Rosenthal type inequality, we present some results of complete convergence for weighted sums of END random variables under mild conditions.

STRONG LIMIT THEOREMS FOR WEIGHTED SUMS OF NOD SEQUENCE AND EXPONENTIAL INEQUALITIES

Some properties for negatively orthant dependent sequence are discussed. Some strong limit results for the weighted sums are ob- tained, which generalize the corresponding results for independent se- quence and negatively associated sequence. At last, exponential inequal- ities for negatively orthant dependent sequence are presented.

Strong Limit Theorems for Weighted Sums of Negatively Associated Random Variables

Let {X n , n ≥ 1} be a sequence of negatively associated random variables with identical distribution. Some properties for negatively associated sequences are discussed. Some strong convergence results for the weighted sums are obtained, which generalize the corresponding results for independent sequences without adding extra conditions. In addition, strong stability for weighted sums of negatively associated random variables is studied.

The Bahadur representation for sample quantile under NOD sequence

In this paper, we investigate the Bahadur representation of sample quantile based on negatively orthant dependent sequence, which is weaker than negatively associated sequence. Our results extend and improve the results of Ling [(2008), ‘The Bahadur Representation for Sample Quantiles Under Negatively Associated Sequence’, Statistics & Probability Letters, 78, 2660–2663].

A Note on the Inverse Moment for the Non Negative Random Variables

Let {Zn} be a sequence of non negative random variables satisfying a Rosenthal-type inequality and , where {Mn} is a sequence of positive real numbers. By using the Rosenthal-type inequality, the inverse moment E(a + Xn)− α can be asymptotically approximated by (a + EXn)− α for all a > 0 and α > 0. Furthermore, we show that E[f(Xn)]− 1 can be asymptotically approximated by [f(EXn)]− 1 for a function f( · ) satisfying certain conditions. Our results generalize and improve some corresponding results, which can allow immediate applications to compute the inverse moments for the non negative random variables whose distributions are such as Binomial distribution, Poisson distribution, Gamma distribution, etc.

Complete moment convergence for randomly weighted sums of martingale differences

In this article, we obtain the complete moment convergence for randomly weighted sums of martingale differences. Our results generalize the corresponding ones for the nonweighted sums of martingale differences to the case of randomly weighted sums of martingale differences.MSC:60G50, 60F15.