Orthant Dependent Random Variables Research Articles

Complete Moment Convergence for Arrays of Rowwise Widely Orthant Dependent Random Variables

In this paper, complete moment convergence for widely orthant dependent random variables is investigated under some mild conditions. For arrays of rowwise widely orthant dependent random variables, the main results extend recent results on complete convergence to complete moment convergence. These results on complete moment convergence are shown to yield new results on complete integral convergence.

On the convergence rates of kernel estimator and hazard estimator for widely dependent samples

In this paper, we establish a Bernstein-type inequality for widely orthant dependent random variables, and obtain the rates of strong convergence for kernel estimators of density and hazard functions, under some suitable conditions.

Some convergence properties for partial sums of widely orthant dependent random variables and their statistical applications

In this paper, we present the $$L_p$$ convergence for partial sums $$S_n=\sum _{k=1}^nX_k$$ under the Cesaro uniform integrability condition and the complete convergence for the maximum of $$S_n$$ for sequences of widely orthant dependent random variables $$\{X_n,n\ge 1\}.$$ Some of the results extend the corresponding ones in reference. As applications, we get the complete consistency and the strong consistency for the estimator in a nonparametric regression model.

An exponential inequality and its application to M estimators in multiple linear models

In the paper, an exponential inequality for widely orthant dependent random variables is established without bounded condition. By using the inequality, we further investigate the strong linear representation for the M estimator of the regression parameter vector in linear regression models with widely orthant dependent random errors under some general conditions. In addition, we have conducted comprehensive simulation studies to demonstrate the validity of obtained theoretical results.

On the strong convergence properties for weighted sums of negatively orthant dependent random variables

In the paper, the strong convergence properties for two different weighted sums of negatively orthant dependent (NOD) random variables are investigated. Let {X n , n ≥ 1} be a sequence of NOD random variables. The results obtained in the paper generalize the corresponding ones for i.i.d. random variables and identically distributed NA random variables to the case of NOD random variables, which are stochastically dominated by a random variable X. As a byproduct, the Marcinkiewicz-Zygmund type strong law of large numbers for NOD random variables is also obtained.

Complete moment convergence for negatively orthant dependent random variables and its applications in statistical models

In this paper, a general result on complete moment convergence for arrays of rowwise negatively orthant dependent random variables is obtained. In addition, we present some sufficient conditions to prove the complete moment and complete convergences for the variables. As applications, the complete consistency for the estimators of nonparametric and semiparametric regression models based on negatively orthant dependent errors is established by using the complete convergence that we established. A simulation to study the numerical performance of the consistency for the nearest neighbor weight function estimator in semiparametric regression model is given. Our results generalize and improve some corresponding ones for independent random variables and negatively associated random variables.

Precise large deviations for widely orthant dependent random variables with different distributions

Let X_{i}, igeq1 be a sequence of random variables with different distributions F_{i}, igeq1. The partial sums are denoted by S_{n}=sum_{i=1}^{n} X_{i}, ngeq1. This paper mainly investigates the precise large deviations of S_{n}, ngeq1, for the widely orthant dependent random variables X_{i}, igeq1. Under some mild conditions, the lower and upper bounds of the precise large deviations of the partial sums S_{n}, ngeq1, are presented.

On complete and complete moment convergence for weighted sums of widely orthant dependent random variables

In this article, the complete convergence for weighted sums of widely orthant dependent (WOD, in short) random variables without identical distribution is investigated. In addition, the complete moment convergence for weighted sums of WOD random variables is also obtained. The results obtained in the paper generalize some corresponding ones for some dependent random variables.

Moment Inequalities for $m$-NOD Random Variables and Their Applications

The concept of $m$-negatively orthant dependent ($m$-NOD) random variables is introduced, and the moment inequalities for $m$-NOD random variables, especially the Marcinkiewicz--Zygmund-type inequa...

On the complete convergence of weighted sums for widely orthant dependent random variables

On the complete convergence of weighted sums for widely orthant dependent random variables

Almost sure convergence for weighted sums of WNOD random variables and its applications to non parametric regression models

ABSTRACTIn this article, some results on almost sure convergence for weighted sums of widely negative orthant dependent (WNOD) random variables are presented. The results obtained in the article generalize and improve the corresponding one of J. Lita Da Silva. [(2015), “Almost sure convergence for weighted sums of extended negatively dependent random variables.” Acta Math. Hungar. 146 (1), 56–70]. As applications, the strong convergence for the estimator of non parametric regression model are established.

Asymptotic Property of M Estimator in Classical Linear Models Under Dependent Random Errors

In this paper, we first establish a useful result on strong convergence for weighted sums of widely orthant dependent (WOD, in short) random variables. Based on the strong convergence that we established and the Bernstein type inequality, we investigate the strong consistency of M estimators of the regression parameters in linear models based on WOD random errors under some more mild moment conditions. The results obtained in the paper improve and extend the corresponding ones for negatively orthant dependent random variables and negatively superadditive dependent random variables. Finally, the simulation study is provided to illustrate the feasibility of the theoretical result that we established.

Weak and strong laws of large numbers for arrays of rowwise END random variables and their applications

In the paper, the Marcinkiewicz–Zygmund type moment inequality for extended negatively dependent (END, in short) random variables is established. Under some suitable conditions of uniform integrability, the $$L_r$$ convergence, weak law of large numbers and strong law of large numbers for usual normed sums and weighted sums of arrays of rowwise END random variables are investigated by using the Marcinkiewicz–Zygmund type moment inequality. In addition, some applications of the $$L_r$$ convergence, weak and strong laws of large numbers to nonparametric regression models based on END errors are provided. The results obtained in the paper generalize or improve some corresponding ones for negatively associated random variables and negatively orthant dependent random variables.

Complete moment convergence of widely orthant dependent random variables

ABSTRACTIt is known that the dependence structure of widely orthant dependent (WOD) random variables is weaker than those of negatively associated (NA) random variables, negatively superadditive dependent (NSD) random variables, negatively orthant dependent (NOD) random variables, and extended negatively dependent (END) random variables. In this article, the results of complete moment convergence and complete convergence are presented for WOD sequence under the same moment conditions as independent sequence in classical result (Chow 1988).

Complete convergence for arrays of rowwise widely orthant dependent random variables and its applications

In this paper, we study complete convergence for arrays of rowwise widely orthant dependent (WOD) random variables. Some general results on complete convergence for arrays of rowwise WOD random variables are established, which generalize the corresponding ones for extended negatively dependent random variables. As applications, we present some corollaries on complete convergence for WOD random variables, and present a result on complete consistency for the estimator in a nonparametric regression model based on WOD errors.

Strong convergence properties for arrays of rowwise negatively orthant dependent random variables

Abstract Let {Xni , i ≥ 1, n ≥1} be an array of rowwise negatively orthant dependent random variables which is stochastically dominated by a random variable X. Wang et al. [15. Complete convergence for arrays of rowwise negatively orthant dependent random variables, RACSAM, 106 (2012), 235–245] studied the complete convergence for arrays of rowwise negatively orthant dependent random variables under the condition that X has an exponential moment, which seems too strong. We will further study the complete convergence for arrays of rowwise negatively orthant dependent random variables under the condition that X has a moment, which is weaker than exponential moment. Our results improve the corresponding ones of Wang et al. [15].

Complete moment convergence for weighted sums of negatively orthant dependent random variables

In this paper, the complete moment convergence and the integrability of the supremum for weighted sums of negatively orthant dependent (NOD, in short) random variables are presented. As applications, the complete convergence and the Marcinkiewicz-Zygmund type strong law of large numbers for NODrandom variables are obtained. The results established in the paper generalize some corresponding ones for independent random variables and negatively associated random variables.

Complete convergence of moving average process based on widely orthant dependent random variables

In this paper, we investigate the complete convergence of moving average process $$\sum \nolimits _{i=-\infty }^{\infty }a_iY_{i+n}, n\ge 1$$ , where $$\{Y_i,-\infty<i<+\infty \}$$ is a doubly infinite sequence of random variables and $$\{a_n,-\infty<n<+\infty \}$$ is an absolutely summable sequence of real numbers. The results obtained in the paper extend and improve the corresponding ones in Qiu and Chen (Acta Math Sci 35A(4):756–768, 2015) from extended negatively dependent (END) setting to widely orthant dependent (WOD) setting.

Complete convergence and complete moment convergence for widely orthant-dependent random variables

ABSTRACTIn this paper, we first establish the complete convergence for weighted sums of widely orthant-dependent (WOD, in short) random variables by using the Rosenthal type maximal inequality. Based on the complete convergence, we further study the complete moment convergence for weighted sums of arrays of rowwise WOD random variables which is stochastically dominated by a random variable X. The results obtained in the paper generalize the corresponding ones for some dependent random variables.

On the exponential inequalities for widely orthant-dependent random variables

ABSTRACTIn this work, we establish some exponential inequalities for widely orthant-dependent random variables. We also obtain the convergence rate O(n− 1/2ln 1/2n) for the strong law of large numbers for widely orthant-dependent random variables.