The asymptotic properties of the estimators in a semiparametric regression model

Abstract

In this paper, we investigate the parametric component and nonparametric component estimators in a semiparametric regression model based on ϕ-mixing random variables. The r th mean consistency, complete consistency, uniform r th 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 ϕ-mixing random errors.

Statistical inference for a heteroscedastic regression model with φ-mixing errors

“…The concept of u-mixing random variables was introduced by Dobrushin (1956) and have been studied by many scholars. For instance, one can refer to Dobrushin (1956) for central limit theorem, Peligrad (1985) for weak invariance principles, Yang (1995) for almost sure convergence and probability inequalities, Shen, Wang, and Ling (2014) for complete convergence, Li, Yin, and Wei (2008) for asymptotic normality, Wang et al (2009) for moment inequality, Wang and Hu (2012) for some Baum-Katz type results, Yang et al (2012), Yang, Wang, and Hu (2014) for Berry-Ess een bound of sample quantiles, Hu et al (2012) for Bernstein type inequalities and inverse moments, Shen (2014) for asymptotic approximation of inverse moments, for the rate of complete convergence, Wang, Wang, and Wang (2017) for exponential inequalities, Wang, Ge, and Wu (2019), for asymptotic properties, etc.…”