Orthant Dependent Random Variables Research Articles

Strong laws for weighted sums of widely orthant dependent random variables and applications

Abstract In this study, the strong law of large numbers and the convergence rate for weighted sums of non-identically distributed widely orthant dependent random variables are established. As applications, the strong consistency for weighted estimator in nonparametric regression model and the rate of strong consistency for least-squares estimator in multiple linear regression model are obtained. Some numerical simulations are also provided to verify the validity of the theoretical results.

Complete moment convergence for widely orthant dependent random variables

The author studies the complete moment convergence for widely orthant dependent random variables. The obtained result in this paper improves the corresponding one of Chen and Sung [A Spitzer-type law of large numbers for widely orthant dependent random variables, Statist. Probab. Lett. 154 (2019), pp. 108544] by obtaining a much stronger conclusion under the same conditions.

Complete convergence for weighted sums of widely negative orthant dependent random variables under the sub-linear expectations

. In this article, we study and establish complete convergence for widely negative orthant dependent random variables under the sub-linear expectations, which extend some complete convergence theorems for widely negative orthant dependent random variables from the classical probability space to sub-linear expectation space.

Almost sure convergence for a class of dependent random variables under sub-linear expectations

<abstract><p>This article aimed to investigate the almost sure convergence theorem of widely negative orthant dependent (WNOD) random variables under sub-linear expectation space. The conclusions in this essay are an extension of the corresponding conclusions in the classical probability space.</p></abstract>

Law of the single logarithm for randomly weighted sums of dependent sequences and an application

<abstract><p>In this work, the law of the single logarithm for randomly weighted sums of widely orthant dependent random variables was studied, which improved and generalized some corresponding results in the literature. As an application, the rate of complete convergence for random weighting estimation with widely orthant dependent samples was obtained under general assumptions. Some numerical analyses were also conducted to confirm the theoretical results.</p></abstract>

Complete convergence for randomly weighted sums of dependent random variables and an application

. In this article, we establish complete convergence for randomly weighted sums of negatively orthant-dependent random variables. We also establish complete convergence for the maximums of randomly weighted sums of negatively associated random variables. As a corollary, a Marcinkiewicz-Zygmund-type strong law for randomly weighted sums of negatively associated random variables is obtained. The results can be applied to the bootstrap sample means, and an open problem in a convergence rate of the bootstrap sample means posed by Csörgő (2004) is solved completely.

Complete [formula omitted]-moment convergence for maximal randomly weighted sums of arrays of rowwise widely orthant dependent random variables and its statistical applications

In this paper, we study the complete f-moment convergence for maximal randomly weighted sums of arrays of rowwise widely orthant dependent random variables under some general conditions. The results obtained in the paper extend and improve some previous known ones. As applications of our main results, we not only present convergence for the state observers of linear-time-invariant systems but also obtain complete consistency for the estimators of errors-in-variables regression models based on widely orthant dependent errors. We further perform a numerical simulation to verify the validity of the theoretical results.

Strong Consistency of Least-Squares Estimators in the Simple Linear Errors-in-Variables Regression Model with Widely Orthant Dependent Random Variables

ABSTRACT In this paper, we establish some results on strong consistency for the least square estimator in a simple linear errors-in-variables regression models based on widely orthant dependent errors. The results obtained in the paper generalize or improve the corresponding ones for dependent random variables. We also carry out some simulation studies to verify the validity of our theoretical results.

Complete convergence for weighted sums of widely negative dependent random variables under the sub-linear expectations

Using different research methods than probability space, this article investigates complete convergence for weighted sums of widely negative dependent random variables under sub-linear expectations. The major findings of this study are expansions of complete convergence for weighted sums of widely orthant-dependent random variables in the standard probability space.

Complete convergence and complete integral convergence for randomly weighted sums under the sublinear expectations

The complete convergence and complete integral convergence for randomly weighted sums when the weight is A n i under the sublinear expectations are established in this article. The major findings of this study are expansions of complete convergence and complete moment convergence for widely orthant-dependent (WOD) random variables in the traditional probability space.

Strong Convergence for Weighted Sums of Widely Orthant Dependent Random Variables and Applications

Strong Convergence for Weighted Sums of Widely Orthant Dependent Random Variables and Applications

Complete convergence and complete moment convergence for widely negative orthant dependent random variables under the sub-linear expectations

In this work there is considered complete convergence and complete moment convergence for widely negative orthant dependent random variables under the sub-linear expectations. The presented results concern the weighted sums of these random variables and extend the corresponding results in classical probability space to the case of sub-linear expectation space.

Marcinkiewicz–Zygmund type strong law of large numbers for weighted sums of random variables with infinite moment and its applications

In this work, the Marcinkiewicz–Zygmund type strong law of large numbers for weighted sums of widely orthant dependent random variables is established under mild conditions including infinite variance. As applications, some new results such as the Cesàro strong law of large numbers, the strong consistency of the least squares estimator in multiple linear regression models, and the strong consistency of the wavelet estimator in nonparametric regression models are presented. Simulation studies are also provided to support the theoretical results.

NEW TAIL PROBABILITY TYPE INEQUALITIES AND COMPLETE CONVERGENCE FOR WOD RANDOM VARIABLES WITH APPLICATION TO LINEAR MODEL GENERATED BY WOD ERRORS

In this paper, we prove an exponential type inequality for unbounded Widely Orthant Dependent (WOD) random variables. Then we will use this inequality for establishing the almost complete convergence for a sequence of widely dependent random variables (WOD). As an application, we combine Markov inequalities and the new exponential inequality to discuss almost complete convergence of errors generated by a sequence of dependent random variables (WOD) in linear models.

Complete convergence for maximum of weighted sums of WNOD random variables and its application

In this paper, the complete convergence for maximum of weighted sums of widely negative orthant dependent (WNOD) random variables are investigated. Some sufficient conditions for the convergence are provided and a relationship between the weight and the boundary function is revealed. Additionally, a Marcinkiewicz-Zygmund type strong law of large number for weighted sums of WNOD random variables is obtained. The results obtained in this paper generalize some corresponding ones for independent and some dependent random variables. As an application, the strong consistency for the weighted estimator in a non-parametric regression model is established. MR(2010) Subject Classification: 60F15; 62G05.

Complete consistency for the weighted least squares estimators in semiparametric regression models

In this article, we consider the semiparametric regression model where are known fixed design points, β is an unknown parameter to be estimated, and are unknown functions defined on a compact set. Assume that the random errors are zero mean widely orthant dependent (WOD, for short) random variables. Under some suitable conditions, we investigate the complete consistency for the least squares estimators (LSE, for short) and the weighted least squares estimators (WLSE, for short) of β and In addition, a numerical simulation is given to study the numerical performance based on finite samples.

Complete moment convergence forweighted sums of widely orthant dependent random variables and its application in nonparametric regression model

In this paper, the complete moment convergence of weighted sums for widely orthant dependent (WOD, in short) random variables are established. The results obtained in the paper generalize and improve some known ones. As an application of the main results, we present a result on complete consistency for the weighted estimator in a nonparametric regression model based on WOD errors.

Kernel density estimation under widely orthant dependence

The kernel density estimator for widely orthant dependent random variables is studied. The exponential inequalities and the exponential rate for the estimator of a density function with a uniform version over compact sets are investigated. Further, the consistency of the estimator is proved. The results are generalizations of some existing outcomes for both associated and negatively associated samples. The convergence rate of the kernel density estimator is illustrated via a simulation study. Moreover, a real data analysis is presented.

Further Spitzer\u2019s law for widely orthant dependent random variables

The Spitzer’s law is obtained for the maximum partial sums of widely orthant dependent random variables under more optimal moment conditions.

Complete moment convergence for weighted sums of widely orthant-dependent random variables and its application in nonparametric regression models

Complete moment convergence for weighted sums of widely orthant-dependent random variables and its application in nonparametric regression models