On the consistency of the P–C estimator in a nonparametric regression model

Yi Wu, Xuejun Wang () and Narayanaswamy Balakrishnan
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Yi Wu: Anhui University
Xuejun Wang: Anhui University
Narayanaswamy Balakrishnan: McMaster University

Statistical Papers, 2020, vol. 61, issue 2, No 17, 899-915

Abstract: Abstract 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.

Keywords: Extended negatively dependent random variables; P–C estimator; Nonparametric regression; Convergence rate; Consistency; 62G05 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s00362-017-0966-9

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