Asymptotic Properties Of Local Linear Estimators For Semi-functional Partial Linear Regression Model

With the development of times and scientific technological progress, scientific researchers have expanded their way of data collection and have improved their ability. At the same time, the data they collect have clear functional characteristics.For example, spectrum data of pork in the food industry; daily average load data in power industry; economic data for multiple indicators across multiple regions; the temperature and precipitation data in the area and so on. Therefore, the study of functional data has become one of the focuses of current statistical research.In this thesis, we investigate the asymptotic properties of semi-functional partial linear regression model based on local linear method, the details mainly composed of two parts:Firstly, based on the local linear method we establish the estimator of semi-functional partial model which we derive almost sure convergence for the functional non-parametric and asymptotic normality of the parametric part. Finally,the simulation results are compared with the classical Nadarage-Watson kernel estimation method, the results show the local linear method is more effective than the kernel estimation method across the box plot. For the parameter part, we test the asymptotic normality of the estimator by histogram.Secondly, we investigate the prediction analysis for the temperature records based on functional non-parametric method. We mainly analyzes the average monthly temperature of the Anhui Province from January 1955 to December 2010 based on the kernel regression estimation method,establish functional non-parametric model and forecast the temperature in 2010. At the same time, the finite dimensional nonparametric regression model and the functional nonparametric model are compared from the mean square variance of the predicted value and the predicted temperature curve, and the superiority of the function nonparametric model is obtained.