Statistical Inference Of Functional-Coefficient Models And Its Application

All kinds of the methods are proposed to estimate the nonparametric regression function, such as the kernel method, the local polynomial estimators, the smoothing spline, and the series estimators. The essence of the above estimating methods is local estimator or local smoothing technique. In general, the non-parametric regression function is well estimated by the above methods when X is one dimension. But the multivariable nonparametric regression function could not be well estimated by the local estimator because there is only a little data in the local fields of the high dimension regression variable X. This phenomenon is said to be 'the curse of dimension'. Due to a lot of the high dimension data is often happened, the analysis of high dimension data is one of the aspects in which a lot of statisticians are interested. Recently a lot of methods for high dimension data are discovered. There are essentially two approaches: the first is largely concerned with function approximation and the second with dimension reduction. The functional coefficient model, which is the function approximation method, is discussed in this paper. The functional coefficient model is widely applied to the analysis of longitudinal data, nonlinear time series and the biologic data. Recently many of statisticians have been interested in the functional coefficient model because of its simplifying structure, meaningful interpretation and wide application.In the chapter 2, estimators of parameters of linear functional coefficient structural model under interval-censored covariate studied. By constructing conditional mean of the interval censored covariate, the estimators of parameters are obtained by weighted least square method and its consistencies are proved when the distribution of covariate is given. In the chapter 3, first introduces estimator of functional coefficient autoregressive model and local linear estimation method and its asymptotic normality forα-mixing samples is given and improved selected method of parameters, then studies application of FAR model in stock market, finally compared goodness of fit between AR and FAR models by generalized likelihood ratio method, and then forecast result. In the last chapter, investigated stationary condition of new model, by the back-fitting procedure the estimation method of new model is given. Finally, extensive simulation is conducted to examine the performance of the proposed fitting procedure.