Nonparametric Regression Models Estimators In Reciprocal Inverse Gaussian Kernel

Nonparametric Regression Models,one of the key research projects in the field of statistics,are widely applied to medicine,health,industry,economic administration,geology and weather for that these models do well in fitting the actual date comparing to the traditional Parametric Regression Model.In this paper we mainly discussed the estimators of the General nonparametric regression models.The research works in this paper mainly include the following two respects:1.In the regularity condition,we discussed the large sample properties,including the asymptotic normality and the uniform almost sure convergence,of the Reciprocal Inverse Gaussian kernel density estimator proposed by Scaillet.We proved the asymptotic normality by applying Liapounov central-limit theorem.Meanwhile,we proved the uniform almost sure convergence of this estimator by applying Borel-Cantelli lemma and Bernstein inequation.2.We studied the estimator of regression function for the general Nonparametric Regression Models.Firstly,based on the Reciprocal Inverse Gaussian kernel density estimator proposed by Scaillet,we proposed a asymmetric kernel regression function estimator,that's Reciprocal Inverse Gaussian kernel regression estimator of which the nonparametric model support sets is(0,?).Secondly,we discussed the large sample properties,including the asymptotic normality and the uniform almost sure convergence,of the Reciprocal Inverse Gaussian kernel regression estimator.Finally,by simulation studies and real data application,we research that the proposed estimator's performance in the limited samples.