In this paper, we investigate the nonparametric regression model based on extended negatively dependent errors. Some consistency results for the estimator of the regression function g(x) are presented, including the rates of strong consistency and complete consistency, and the mean convergence. The results obtained in this paper improve and extend the corresponding ones of Yang and Wang (Acta Math Appl Sin 22(4):522–530, 1999) and Priestley and Chao (J R Stat Soc B 34:385–392, 1972). Finally, we present a numerical simulation study to verify the validity of the results established here.
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The authors are most grateful to the Editor-in-Chief and anonymous referees for a careful reading of the manuscript and for making valuable suggestions which helped in improving an earlier version of this paper. This work was supported by the National Natural Science Foundation of China (11671012, 11501004, 11501005), the Natural Science Foundation of Anhui Province (1508085J06) and The Key Projects for Academic Talent of Anhui Province (gxbjZD2016005).
Shen AT, Zhang Y, Volodin A (2015) Applications of the Rosenthal-type inequality for negatively superadditive dependent random variables. Metrika 78:295–311MathSciNetCrossRefMATHGoogle Scholar
Shen AT, Yao M, Wang WJ, Volodin A (2016) Exponential probability inequalities for WNOD random variables and their applications. RACSAM 110:251–268MathSciNetCrossRefMATHGoogle Scholar
Wang SJ, Wang XJ (2013) Precise large deviations for random sums of END real-valued random variables with consistent variation. J Math Anal Appl 402:660–667MathSciNetCrossRefMATHGoogle Scholar
Wang XJ, Li XQ, Hu SH, Wang XH (2014) On complete convergence for an extended negatively dependent sequence. Commun Stat Theory Methods 43(14):2923–2937MathSciNetCrossRefMATHGoogle Scholar
Wang XJ, Zhen LL, Xu C, Hu SH (2015) Complete consistency for the estimator of nonparametric regression models based on extended negatively dependent errors. Statistics 49(2):396–407MathSciNetCrossRefMATHGoogle Scholar
Wu YF, Cabrea MO, Volodin A (2014) Complete convergence and complete moment convergence for arrays of rowwise end random variables. Glas Mat 49(69):449–468MathSciNetGoogle Scholar
Yang SC, Wang YB (1999) Strong consistency of regression function estimator for negatively associated samples. Acta Math Appl Sin 22(4):522–530MATHGoogle Scholar