Non-parametric Statistics

  • 申立勇
  • Created: 2014-12-08
Non-parametric Statistics


Course No.S070103ZJ006

Course CategoryProfessional Basic Course


PrerequisitesMathematical analysisAdvanced algebraProbability 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 methodBy integrated explaining theory and instance analysis and combination programmingit 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 ofRobin(1988),Li(1996);

Estimation of nonparametric function: the method of Andrew (1994)

A Feasible Semiparametric Efficient Estimator

Specification Test in Partially Linear ModelsFan and Li1996),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


[1] Prakasa Rao, B. L. S., Nonparametric Functional EstimationAcademic Press, New York, 1993.

[2] HardleW, LiangH and Gao J. Partially Linear Models. Berlin: Physica- Verlag, 2000.

[3] Qi Li and Jeffrey S. Racine Nonparametric Econometrics. Princeton University Press. 2007.

AuthorZhihua Sun (School of Mathematical Sciences, GUCAS)

DateJune, 2009