Partial Linear Model And Its Application

Partial linear model is a significant model which has been used in many fields. It wasfirst proposed by Engle et al in1986when they were researching the practical problem onhow meteorological conditions on the power demand. And ever since, many scholars beganto explore the parameters and non parameter of the model and they had achieved a series ofimportant results. Since the semi parametric model is the union of the parametric andnonparametric regression, it shares their both advantages. For example, the semiparametric model can solve the "dimension disaster", which means it is able to eliminatethe phenomenon that the fitting effect becomes worse quickly led by rapidly increasingerror. Statisticians are searching for methods that can both reduce the dimension of data andkeep the merit of the nonparametric smooth method. In recent years, many domestic andforeign statisticians are keen to researching on the partial linear model, which makes itbecome one of the hot topic in the field of statistics. This paper is mainly about the partiallinear model and its application. And the contents are as follows:The first chapter is introduction. It simply has introduced some theoretical knowledgeof the partial linear model and the partial linear model with missing data, including thepartial linear model method, the partial linear model test, missing data, serial correlationtest, empirical likelihood method and the related research status.The second chapter, it has applied the partial linear model to analysis and predictionof the air quality index, and has concluded that the prediction results of partially linearmodel is better.The third chapter, it has applied the partial linear model to analysis and application ofthe air quality index of fine particles in PM2.5. Through the empirical analysis, it finds thatthe fitting effect of linear model of partially linear model is much better than general andquadratic polynomial regression model.The fifth chapter, it has made a summary and outlook, and also has put forward thefurther research plan on the partially linear model missing data.