Asymptotic Characteristic Of Varying Coefficients Structural EV Model With Time Series

Nonparametric regression is one of the most important estimation method in regression analysis. For a regression model:Y=f(x)+ε, nonparametric regression has not specific assumptions for the form of f(x), but some properties of the f(x) must be assumed. For example, f(x) is a smooth function, etc. Nonparametric regression can reduce the error of model effectively and is one promotion of parametric regression. The research and apply about time series often appear in economics and practice. About linear stationary time series, when the coefficient sequence is supposed suitably, it can include different situation. Such as short dependent, long dependent and independent. Therefore, the research has theoretical and application value. On the other hand, people have put forward many methods to estimate f(x), such as nuclear estimation, local polynomial estimation, smooth spline approximation, orthogonal series approximation and so on. In this paper, when model error is a time series, we study the function estimation of varying coefficients structural EV model Y=β0(t)+xTβ1(t)+e, X=x+μ. Further, to solve the "curse of dimensionality", we need a variable selection for coefficient functions and select significant variables for the regression variable. This paper is structured as follows:Chapter one is the introduction. First, it introduces the model in this paper and some commonly used nonparametric estimation method. Then, ideas and methods are introduced. At last, it introduces the present research about varying coefficient EV models and related work of this paper.Chapter two, researches the the parameters estimation of P-dimension varying coef-ficient EV(error-in-variable) model by the adjust weighted LS estimators(AWLSE) method when the model error is time series. And consistency, asymptotically normal and the conver-gence rate are obtained. A simulation study illustrates our AWLSEs have good performance.Chapter three, mainly studies the variable selection of such a model. First of all, make a smooth B-spline approximation to the varying coefficient. Then select significant variables by penalty least squares method.In the fourth chapter, the conclusion is showed, and some problems we need study later are given.