Non-parametric Statistics

• 申立勇
• Created: 2014-12-08
 Non-parametric Statistics Course No.：S070103ZJ006 Course Category：Professional Basic Course Period/Credits：40/2 Prerequisites：Mathematical analysis、Advanced algebra、Probability theory and mathematical statistics. Aims & Requirements： This course is a subject foundation requisite course for Ph.D. and Master graduate majoring in Probability Theory and Mathematical Statistics. At the same time, it can be used as elective courses of other disciplines. This course introduces modern relatively- new non-parametric and semi-parametric statistical method。By integrated explaining theory and instance analysis and combination programming，it is expected that students can master the main method  of non-parametric and semi-parametric fields. It is also expected that students can analysis the real data by the studied methods. Primary Coverage： Chapter 1 Nonparametric Density Estimation and Testing Univariate Density Estimation Multivariate Density Estimation Multivariate Density Estimation Chapter 2 Nonparametric Regression Local Constant Kernel Estimation Local Linear/Polynomial Kernel Estimation Functional Coefficient Models Nonparametric Quantile Estimation Nonparametric Model Specification Tests Chapter 3 Partially Linear Models Estimation of regression parameters: The methods of（Robin(1988），Li(1996); Estimation of nonparametric function: the method of Andrew (1994)， A Feasible Semiparametric Efficient Estimator； Specification Test in Partially Linear Models：Fan and Li（1996），Zhu and Ng(2003). Chapter 4 Single-Index Models A General Form of Single-Index Models， Identification Condition, Nonlinear Least Squares Estimator Average Derivative Estimator, Nonparametric Estimation of the Link Function, Specification Test for Parametric Single Index Models, Semiparametric Estimation of Binary Choice Model References：  Prakasa Rao, B. L. S., Nonparametric Functional Estimation。Academic Press, New York, 1993.  Hardle，W, Liang，H and Gao J. Partially Linear Models. Berlin: Physica- Verlag, 2000.  Qi Li and Jeffrey S. Racine Nonparametric Econometrics. Princeton University Press. 2007. Author：Zhihua Sun (School of Mathematical Sciences, GUCAS) Date：June, 2009