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：
[1] Prakasa Rao, B. L. S., Nonparametric Functional Estimation。Academic Press, New York, 1993.
[2] Hardle，W, Liang，H and Gao J. Partially Linear Models. Berlin: Physica- Verlag, 2000.
[3] Qi Li and Jeffrey S. Racine Nonparametric Econometrics. Princeton University Press. 2007.
Author：Zhihua Sun (School of Mathematical Sciences, GUCAS)
Date：June, 2009
