Non-parametric Regression Function (?) Mixed Error Estimates

Nonparametric regression model is an important statistical model which was developed in the 1970s. It is widely used in practical problems, as the form of the regression function in the nonparametric model is free and the limits to random variable (X, Y) are fewer. In the past several decades, many researchers have studied it, and obtained a large number of results. Based on the existing papers, this paper studied the large sample properties of weighted function estimator and wavelet estimator of fixed design nonparametric regression model under p mixing errors. This paper is organized as follows:Firstly, this paper gave a brief introduction about the historical background and current situation of development of regression model, especially introduced the current situation of the estimation of non-parametric regression model, and also introduced the historical background of wavelet method.Secondly, consider non-parametric regression model: Where ti∈[0,1], i= 1,2,···n are fixed design points, regression function g(·) is an unknown function, random error sequence {εi,i=1,2,···n} is p mixing which satisfied E{εi)= 0, E(εi2)=σ2<∞,i=1,2,···n. We discussed the strong convergence of weighted sums of (?)-mixing random sequences and obtained some sufficient conditions for the strong consistency of the weighted function estimator of the model.Finally, this paper discussed the large sample properties of wavelet estimator of the above model under identically distributed and different distributed p mixing errors. Under suitable conditions, the asymptotic unbiasedness, mean square consistency, strong consistency and asymptotic normality are obtained.