The Asymptotic Property On Local Polynomial Estimation Of Nonparametric Regression Function For (?)-Mixing Errors

Regression models are widely applied to industry and agriculture, meteorology, economic management, as well as medicine hygiene and so on. Meanwhile because of the needs of practical application, the regression models are developed. The model develops from initial parametric regression models to nonparametric models, also develops to the semiparametric regression models. And the nonparametric models is based on data, the form of its regression function is discretionary, so it has a great adaptability. Semiparametric regression models are a statistical model between parametric models and nonparametric models, has some merits of parametric regression models and nonparametric regression models. It has greater adaptability and stronger explanatory ability than the other two regression models.This dissertation is based onρ~ -mixing samples which is a kind of broad dependent mixing samples, it studies the local polynomial estimation of unknown function in fixed design nonparametric regression model and unknown parametric and unknown function in semiparametric regression model. Given the asymptotic bias and the asymptotic variance of estimation, moreover obtained the asymptotic normality of the estimation under certain condition using small-block and large-block arguments. And estimated the unknown quantity using the methods of least square estimation and local polynomial estimation, obtained the consistency of estimation under certain condition.