On The Fixed Design Non-parametric Regression Model For Dependent Samples

Nonparametric regression model developed in the1970s, is a very important one statistical model. In the form of the model regression function is less arbitrary and restrictions on the distribution of the random variable, Although the regression results epitaxy difficult, but fit better, you can better describe the sample data reflected the non-linear characteristics, Therefore widely used in the actual problem.In nonparametric regression model, many scholars have studied the situation when the error is independent type, however, in many practical problems model errors are often not independent, For theoretical and practical needs, many scholars have proposed to discuss various dependent mixing sequence convergence properties, The NA sequences and φ-mixing sequence is one of the more important two dependent series. In this paper, based on non-parametric regression model under fixed design when error is NA sequence and (p-mixing sequence, we discussed the estimated amount of consistency. The main contents are as follows:The first chapter describes the background knowledge of the work done by non-parametric regression model, Yni=g(xni)+εni, i=1,2,…, n,and the work done by scholars, Finally, the article is organized. The second chapter details the non-parametric regression model and given φ-mixing series definition and φ-mixed Rosenthal inequality, Bernstein-type inequality and related assumptions. While taking advantage of inequality proved the estimator of nonparametric regression model mean convergence, uniform convergence, almost sure convergence and convergence rate. The third chapter describes the definitions of the NA sequence and NA sequence Rosenthal inequality, Bernstein-type inequality, Based on the assumption that given in the estimator of nonparametric regression almost sure convergence.Finally, summarizes the work of this paper and gives future research plans.