Statistial Inference For Partial Linear Functional Linear Regression

Because of the needs of solving practical problems, only discussing the classical re-gression models can not be satisfied. Researchers began to explore more complex data and models, so they paid more attention to the functional data and the analysis of them which is as the extension of random variables. In this paper, we introduce a more general class of functional linear models on the basis of formers, which is called partial linear functional linear regression, where the response variable is a scalar, some of the covariates are random vectors and some are functional. In the case, some functional variables are related to responses linearly while other functional variables have more complicated rela-tionships, which are nonlinear. The relation of random vector and the response variable is linear, so as to some of the random process and response variables, but the others are nonlinear.In the part of introduction, we introduce the development background, current situ-ation and the preparation work. In the chapter one, we introduce some regression models of functional data, and then propose a new partial linear functional linear model. In the chapter two, we estimate the three parameters by kernel somoothers and least square method from the view of Karhunen-Loeve. In the chapter three, we investigae the large sample properties of the estimation about the asymptotic normality and rate of conver-gence. In the chapter four, we prove the estimation and asymptotic normality. In the chapter five, our methods are illustrated with a simulation study. In the chapter six, we summarize our paper and give the outlooks.