The asymptotic properties of the estimators in a semiparametric regression model
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In this paper, we investigate the parametric component and nonparametric component estimators in a semiparametric regression model based on \(\varphi \)-mixing random variables. The rth mean consistency, complete consistency, uniform rth mean consistency and uniform complete consistency are established under some suitable conditions. In addition, a simulation to study the numerical performance of the consistency of the nearest neighbor weight function estimators is provided. The results obtained in the paper improve the conditions in the literature and generalize the existing results of independent random errors to the case of \(\varphi \)-mixing random errors.
KeywordsSemiparametric regression model Complete consistency Mean consistency \(\varphi \)-mixing random variables
Mathematics Subject Classification62G05
The authors are most grateful to the Editor-in-Chief Prof. Christine H. Müller and two anonymous referees for careful reading of the manuscript and 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).
- Herrndorf N (1983) The invariance principle for \(\varphi \)-mixing sequences. Zeitschrift fur Wahrscheinlichkeits-theorie und Verwandte 63(1):97–108Google Scholar
- Wang XJ, Hu SH, Yang WZ, Shen Y (2010) On complete convergence for weighted sums of \(\varphi \)-mixing random variables. J Inequalities Appl 2010 (Article ID 372390)Google Scholar
- Wu QY (2006) Probability limit theory for mixing sequences. Science Press of China, BeijingGoogle Scholar