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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. [ABSTRACT FROM AUTHOR]

In this paper, we establish L2-convergence and complete convergence results for the maximum of the partial sum of asymptotically negatively associated random vectors in Hilbert space. In addition, we consider Hájek-Rényi inequality and prove some strong law of large numbers for H-valued asymptotically negatively associated random vectors. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the complete convergence and complete moment convergence of asymptotically almost negatively associated random variables with random coefficients. The obtained results extend and improve the ones of Li, Rao, and Wang (1992), Characiejus and Račkauskas (2016) and Zhang, Chen, and Sung (2017) to the case of AANA random variables with random coefficients. [ABSTRACT FROM AUTHOR]

In this paper, we consider the complete convergence for weighted sums of negatively superadditive-dependent (NSD) random variables without assumptions of identical distribution. Some sufficient and necessary conditions to prove the complete convergence for weighted sums of NSD random variables are presented, which extend and improve the corresponding ones of Naderi et al. As an application of the main results, the Marcinkiewicz–Zygmund type strong law of large numbers for weighted sums of NSD random variables is also achieved. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the complete moment convergence andLrconvergence for maximal partial sums of asymptotically almost negatively associated random variables under some general conditions. The results obtained in the paper generalize some corresponding ones for negatively associated random variables. [ABSTRACT FROM AUTHOR]

The goal of this paper is to establish complete convergence theorems for an array of row-wise END random variables under sub-linear expectation space. As applications of the exponential inequalities, we extend some complete convergence theorems from the traditional probability space to the sub-linear expectation space and our results generalize corresponding results obtained by Hu. [ABSTRACT FROM AUTHOR]

In 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 variableX. The results obtained in the paper generalize the corresponding ones for some dependent random variables. [ABSTRACT FROM AUTHOR]

In this paper, we discuss complete convergence and complete moment convergence results for extended negatively dependent random variables. The obtained theorems not only extend the Baum-Katz type theorem to the case of END random variables, but also improve them. [ABSTRACT FROM AUTHOR]

In this paper, we study the complete moment convergence for arrays of rowwise m-extended negatively dependent (m-END) random variables, which generalizes some corresponding ones for complete convergence. We also give an application to non-parametric regression model based on m-END errors by using the complete convergence that we establish. Finally, the choice of the fixed design points and the weight functions for the nearest neighbor estimator are proposed. We also provide a numerical simulation to verify the validity of our theoretical result. [ABSTRACT FROM AUTHOR]

Under the condition that the Choquet integral exists, we study the complete convergence theorem for negatively dependent random variables under sub-linear expectation space. Two general complete convergence theorems under sub-linear expectation space are obtained, where the coefficient of weighted sum is the general function. This paper not only extends the complete convergence theorem in the traditional probability space to the sub-linear expectation space, but also extends the coefficient of weighted sum as a general function. [ABSTRACT FROM AUTHOR]

In this paper, the complete moment convergence for arrays of rowwise negatively superadditive dependent (NSD, for short) random variables is established. As applications, the complete convergence and the Marcinkiewicz-Zygmund type strong law of large numbers for arrays of rowwise NSD random variables are also obtained. Finally, a numerical simulation is carried out to verify the validity of theoretical results. The results obtained in the paper extend the corresponding ones in the literature. [ABSTRACT FROM AUTHOR]

In this paper, the complete convergence for maximal weighted sums of extended negatively dependent (END, for short) random variables is investigated. Some sufficient conditions for the complete convergence and some applications to a nonparametric model are provided. The results obtained in the paper generalize and improve the corresponding ones of Wang et al. (2014b) and Shen, Xue, and Wang (2017). [ABSTRACT FROM AUTHOR]

In this paper, complete convergence for arrays of row-wise ND random variables under sub-linear expectations is studied. As applications, the complete convergence theorems of weighted sums for negatively dependent random variables have been generalized to the sub-linear expectation space context. We extend some complete convergence theorems from the traditional probability space to the sub-linear expectation space and our results generalize corresponding results obtained by Ko. [ABSTRACT FROM AUTHOR]

Let {Xnk, k ⩾ 1, n ⩾ 1} be an array of rowwise ANA random variables stochastically dominated by a random variable X, and {ank, 1 ⩽ k ⩽ n, n ⩾ 1} be an array of real numbers with for some 0 ⩽ α ⩽ 2. Under the almost optimal moment conditions, the paper shows that In addition, we can get the strong law of large numbers for sequence of ANA random variables as application of our Theorem. [ABSTRACT FROM AUTHOR]

In this paper, some complete convergence and complete moment convergence results for arrays of rowwise negatively superadditive dependent (NSD, in short) random variables are studied. The obtained theorems not only extend the result of Gan and Chen (2007) to the case of NSD random variables, but also improve them. [ABSTRACT FROM AUTHOR]

In this paper, the complete convergence and the complete moment convergence for maximal randomly weighted sums of widely orthant-dependent (WOD, in short) random variables are investigated. By using the main results, we further consider three striking and useful applications in probability and statistics. Our results generalize the corresponding earlier ones. [ABSTRACT FROM AUTHOR]

In this paper, the complete convergence of weighted sums of Lr-mixingale is established, from which the complete convergence of martingale differences is also derived. As statistical applications, non parametric regression model and simpler linear errors-in-variables model with mixingale errors are discussed. [ABSTRACT FROM AUTHOR]

In this paper, we establish several generalized results on complete convergence for martingale difference sequence, which include some well-known results. [ABSTRACT FROM AUTHOR]

In this paper, we establish the complete convergence and complete integral convergence for arrays of row-wise extended independent random variables under sub-linear expectation space with some conditions. At the same time we extend some complete convergence and complete integral convergence theorems from the classical probability space to the sub-linear expectation space. The results generalize corresponding results obtained by Wu et al. (2017). [ABSTRACT FROM AUTHOR]

In this paper, we obtain complete convergence results for Stout type weighted sums of i.i.d. random variables. A strong law for weighted sums of i.i.d. random variables is also obtained. As the applications of the strong law, the strong consistency and rate of the nonparametric regression estimations and the rates of the strong consistency of LS estimators for the unknown parameters of the simple linear errors in variables (EV) model are given. [ABSTRACT FROM PUBLISHER]

In this paper, we study the complete convergence and complete moment convergence for negatively orthant-dependent random variables. Especially, we obtain the Hsu–Robbins-type theorem for negatively orthant-dependent random variables. Our results generalize the corresponding ones for independent random variables. [ABSTRACT FROM AUTHOR]

In this paper, we establish the strong law of large numbers and complete convergence for non-identically distributed WOD random variables. We derive some new inequalities of Fuk–Nagaev type for the sums of non-identically distributed WD random variables. All these results further extend and refine previous ones. [ABSTRACT FROM AUTHOR]

In this paper, we prove the complete convergence for the weighted sums of negatively associated random variables with multidimensional indices. The main result generalizes Theorem 2.1 in Kuczmaszewska and Lagodowski (2011) to the case of weighted sums. [ABSTRACT FROM PUBLISHER]

In this paper, we establish a complete convergence result and a complete moment convergence result for i.i.d. random variables under moment condition which is slightly weaker than the existence of the moment generating function. The main results extend and improve the related known results of Lanzinger (1998) and Gut and Stadtmüller (2011). [ABSTRACT FROM PUBLISHER]

Letbe an array of rowwise ϕ-mixing random variables. A rate of complete convergence for weighted sums of arrays of rowwise ϕ-mixing random variables is obtained without assumption of identical distribution. The techniques used in the paper are the Rosenthal type inequality and the truncated method. As an application, the Baum and Katz type result for arrays of rowwise ϕ-mixing random variables is obtained. [ABSTRACT FROM AUTHOR]

In this article, we study complete and complete integral convergence theorems for weighted sums of arrays of rowwise widely negative dependent random variables under the sub-linear expectations. The presented results are Baum-Katz type theorems that extend the corresponding results in classical probability space to the case of sub-linear expectation space. [ABSTRACT FROM AUTHOR]

In this article, we study strong limit theorems for weighted sums of extended negatively dependent (END, for short) random variables under the sub-linear expectations. We establish some general complete convergence theorems for weighted sums of END random variables under the sub-linear expectations. Our results partly generalize and improve the corresponding ones previously obtained by Cai (Metrika, 68:323-331, 2008), Huang and Wang (J. Inequal. Appl. 233, doi:10.1186/1029-242X-2012-233, 2012) and Wang et al. (RACSAM, 106:235-245, 2012) in the classical probability space to the sub-linear expectation space under weaker moment conditions. [ABSTRACT FROM AUTHOR]

In this article, complete and complete integral convergence theorems are obtained for arrays of row wise widely negative dependent random variables under the sub-linear expectations. We improve the results by (Lin and Feng 2019) and extend some complete moment convergence theorems in (Wu, Wang, and Rosalsky 2018) from the classical probability space to the sub-linear expectation space. [ABSTRACT FROM AUTHOR]

Let { X n i , 1 ≤ i ≤ m n , n ≥ 1 } be an array of independent exponentially distributed random variables with mean λn, and { X n (1) ≤ X n (2) ≤ ⋯ ≤ X n (m n) } be the order statistics of the random variables { X n i , 1 ≤ i ≤ m n }. Limit properties of the ratios { R nij = X n (j) / X n (i) , 1 ≤ i < j ≤ m n } are investigated for fixed sample size mn = m. Specifically, the weak law of large numbers is derived for R n 1 j under some more general conditions, followed by the establishment of its complete convergence. Furthermore, the large deviation principles for both R n 1 j and R n 2 j are formulated. [ABSTRACT FROM AUTHOR]

In this article, some results on the complete moment convergence for maximal randomly weighted sums of extended negatively dependent (END) random variables are established. In some senses, the results obtained in this article extend the corresponding ones of in reference. As an application of the main results, we consider a result on complete consistency for the weighted estimator in a non parametric regression model based on END errors. We also give a simulation to verify the validity of the theoretical result. [ABSTRACT FROM AUTHOR]

In this article, we study complete and complete moment convergence theorems for arrays of rowwise negatively dependent random variables under the sub-linear expectations. The complete and complete moment convergence theorems in the sense of non-additive capacities are established for arrays of rowwise negatively dependent random variables. Our result improves the corresponding result of Wang et al. relative to the classical probability space. [ABSTRACT FROM AUTHOR]

The authors study the strong convergence for sequences of pairwise negatively quadrant dependent (NQD) random variables under some wide conditions, and present some new theorems on the complete convergence and the strong laws of large numbers. The obtained results extend and improve some theorems in existing literature. [ABSTRACT FROM AUTHOR]

In this article, we study complete convergence theorems for weighted sums of negatively dependent random variables under the sub-linear expectations. Our results extend the corresponding results of Sung (2012) relative to the classical probability. [ABSTRACT FROM AUTHOR]

Support that p ⩾ 1, {Yni, 1 ⩽ i ⩽ n, n ⩾ 1} is an array of upper extended negatively dependent random variables, there exist a random variable Y and a constant c satisfying , . If {ani; 1 ⩽ i ⩽ n, n ⩾ 1} is an array of real positive constants satisfying certain conditions, we can obtain the complete convergence for weighted sums of extended negatively dependent random variables under sub-linear expectations. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM PUBLISHER]