In this paper, some basic properties for negatively superadditive-dependent (NSD, in short) random variables are presented, such as the Rosenthal-type inequality and the Kolmogorov-type exponential inequality. Using these properties, we further study the complete convergence for weighted sums of NSD random variables, which generalizes and improves some corresponding ones for independent random variables and negatively associated random variables. Some sufficient conditions to prove the complete convergence for weighted sums of NSD random variables are provided. As an application, the complete consistency of LS estimators in the EV regression model with NSD errors is investigated under mild conditions, which generalizes and improves the corresponding one for negatively associated random variables.

Complete convergence for weighted sums of NSD random variables and its application in the EV regression model

In this paper, we establish strong laws for weighted sums of identically distributed $$\psi $$
 -mixing random variables without any conditions on mixing rate. The classical Kolmogorov strong law of large numbers is extended to weighted sums of $$\psi $$
 -mixing random variables. Two types of weights are considered for the weighted sums. These results are applied to the least-squares estimators in the simple linear errors-in-variables regression model when the errors are $$\psi $$
 -mixing random vectors.

Strong laws for weighted sums of $$\psi $$ ψ -mixing random variables and applications in errors-in-variables regression models

In this paper, the complete convergence and complete moment convergence for arrays of rowwise negatively superadditive dependent (NSD, in short) random variables are investigated. Some sufficient conditions to prove the complete convergence and the complete moment convergence are presented. The results obtained in the paper generalize and improve some corresponding ones for independent random variables and negatively associated random variables.

Complete moment convergence for arrays of rowwise NSD random variables

Mineralocorticoid receptor antagonists: identification of heterocyclic amide replacements in the oxazolidinedione series.

In this paper, an exponential inequality for the maximal partial sums of negatively superadditive-dependent (NSD, in short) random variables is established. By using the exponential inequality, we present some general results on the complete convergence for arrays of rowwise NSD random variables, which improve or generalize the corresponding ones of Wang et al. [28] and Chen et al. [2]. In addition, some sufficient conditions to prove the complete convergence are provided. As an application of the complete convergence that we established, we further investigate the complete consistency and convergence rate of the estimator in a nonparametric regression model based on NSD errors.

Complete convergence for arrays of rowwise negatively superadditive-dependent random variables and its applications

In this paper, Kolmogorov-type inequality for negatively superadditive dependent (NSD) random variables is established. By using this inequality, we obtain the almost sure convergence for NSD sequences, which extends the corresponding results for independent sequences and negatively associated (NA) sequences. In addition, the strong stability for weighted sums of NSD random variables is studied.

Almost sure convergence theorem and strong stability for weighted sums of NSD random variables

In this paper, we study the Marcinkiewicz-type strong law of large numbers, Hajek-Renyi-type inequality and other inequalities for negatively superadditive dependent (NSD) sequences. As an application, the integrability of supremum for NSD random variables is obtained. Our results extend the corresponding ones of Christofides and Vaggelatou (J. Multivar. Anal. 88:138-151, 2004) and Liu et al. (Stat. Probab. Lett. 43:99-105, 1999). MSC:60F15.

/pdf/on-the-strong-convergence-and-some-inequalities-for-2rggf9d1v5.pdf

On the strong convergence and some inequalities for negatively superadditive dependent sequences

In this article, the complete convergence and complete moment convergence for weighted sums of asymptotically negatively associated (ANA, for short) random variables are studied. Several su...

On complete and complete moment convergence for weighted sums of ANA random variables and applications

Maximal inequality for ψ-mixing sequences and its applications

In this paper, we get the Hajek-Renyi-type inequalities for a pairwise NQD sequence, an L
 r
 (r > 1) mixingale and a linear process, which have the concrete coefficients. In addition, we obtain the strong law of large numbers, strong growth rate and the integrability of supremum for the above sequences, which generalize and improve Corollary 2 for L
 r
 (r > 1) mixingale of Hansen.

Hájek-Rényi-type inequality and strong law of large numbers for some dependent sequences

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