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AbstractIn this paper, the Rosenthal-type maximal inequalities and Kolmogorov-type exponential inequality for negatively superadditive-dependent (NSD) random variables are presented. By using these inequalities, we study the complete convergence for arrays of rowwise NSD random variables. As applications, the Baum–Katz-type result for arrays of rowwise NSD random variables and the complete consistency for the estimator of nonparametric regression model based on NSD errors are obtained. Our results extend and improve the corresponding ones of Chen et al. On complete convergence for arrays of rowwise negatively associated random variables. Theory Probab Appl. 2007;52(2):393–397 for arrays of rowwise negatively associated random variables to the case of arrays of rowwise NSD random variables.Keywords: Rosenthal-type maximal inequalityKolmogorov-type exponential inequalitynegatively superadditive-dependent random variablescomplete convergencecomplete consistency2000 Mathematics Subject Classification:: 60F1560E0562G05 AcknowledgementsThe authors are most grateful to the Editor-in-Chief, Associate Editor and anonymous referees for careful reading of the manuscript and valuable suggestions which helped in significantly improving an earlier version of this paper.Supported by the National Natural Science Foundation of China (11201001, 11171001, 11126176), Natural Science Foundation of Anhui Province (1208085QA03, 1308085QA03), Applied Teaching Model Curriculum of Anhui University (XJYYXKC04), Doctoral Research Start-up Funds Projects of Anhui University and the Students Science Research Training Program of Anhui University (KYXL2012007).
Wang et al. (Wed,) studied this question.