Applications Of B Spline In Functional-coefficient Partially Linear Models

Nonparametric methods are developed as more flexible tools for statistician to build more accurate models. With the advantages of very few restrictions on model struc-ture, strong robustness, and data-driven property, nonparametric models are extensively discussed recently. Regarding nonparametric regression models, the most widely used ap-proaches include:kernel method, local polynomial technique, series estimation and spline method(such as smoothing spline, penalized spline and B-spline).Functional-coefficient partially linear regression model is a generalized model by com-bining nonparametric and functional-coefficient regression model. It is proposed aiming to fit the model using the real data of Yingluo River. The most challenging part is that the smoothing variable of the constant part is different from that of the coefficient functions which brings difficulty to estimation. So far the local linear technique and the integrated method have been introduced to estimate all functions in FCPLR model. Although local linear method shows a good statistical property to the local area while in the global area it still needs improvement. B-spline with the appealing statistical properties as a global technique is provided to improve the estimator.This dissertation plans to employ B-spline to estimate all the coefficients of Functional-coefficient partially linear regression model. The least square estimation method and asymptotic normality properties are also discussed with some simulations to illustrate the performance of the proposed technique in FCPLR model.