Estimation And Sequence Correlation Test In Partial Linear Model

In the regression model analysis,the need of random error of the model assumptions,often assumes that the random error is zero mean and variance of the white noise sequence,but in the actual problem analysis,the hypothesis conditions cannot meet.Therefore,it is necessary to carry out a series of tests on the model,such as correlation test and heteroscedasticity test.Only by accurately judging the model,can we estimate the parameters and test the hypothesis of the model,put forward reasonable suggestions and make correct decisions based on the analysis and research of the regression model.As components in a partly linear model of partial linear model and variable coefficient model with variable coefficients,a special case,have the characteristics of the two models,presents the model of its own unique charm,has been widely applied in econometrics and biomedical field.Partial linear models not only have the characteristics that linear models are easy to explain,but also can describe the interaction of covariables,which effectively solves the so-called "dimension curse" problem,plays the role of dimension-reduction,and has more flexible functional form,which has certain research significance and value.This paper mainly studies the partial linear model parameter and nonparametric estimation and correlation of error sequence.In this paper,through two methods,one is a local linear method,the other is a b-spline method,part of the components in a partly linear model parameters,as well as be estimated function part of the estimate of the unknown,through numerical simulation,comparison under the two methods,the advantages and disadvantages of different estimation methods.At the same time,based on B-spline estimation method,the empirical likelihood method proposed by Liu Feng,Chen Min and Zou Jiezhong(2006)[1] was applied to the sequence correlation test of partial linear models.At the same time,the empirical logarithm likelihood ratio statistic was constructed and proved to be asymptotic to be the chi-square distribution.Finally,the sequence correlation under different distribution and different error models was analyzed by Monte Carlo method.