Statistical Models

Spring 2009

Instructor: 田茂再 (Email: mztian(at)ruc.edu.cn)

Office Hours: by appointment

Lectures: Friday, 2:00-5:00 p.m., 0308 Mingde Main Building

Teaching Assistant: 程晓月 (Email: chengxy(at)ruc.edu.cn)

Text Book:

Searle, S. R. Matrix Algebra Useful for Statistics

Seber G. A. F. Linear Regression Analysis

Graybill, F. A. The Theory and Applications of the Linear Model

Part 2 —- Nonparametric & Semiparametric Models Wolfgang Hardle, et al. Nonparametric and Semiparametric Models

Wolfgang Hardle. Smoothing Techniques with Implementation in S

Mar. 27
1. Matrix Algebra
2. General Linear Model
Apr. 3
1. The Weighted Least Square Estimation
2. The Best Linear Unbiased Estimator (b.l.u.e.)
3. MLE
4. Partitioning Total Sum of Squares
Apr. 10
1. Introduction to Nonparametric & Semiparametric Models
2. Histogram
Apr. 17
1. Average Shifted Histogram
2. Kernel Density Estimation (properties, parameter selection, kernel choosing, multivariate situation)
May 8
1. Nonparametric Regression
2. Multivariate Kernel Density Estimation
3. Local Polynomial Regression
4. k – Nearest Neighbor Estimation
May 15
1. Dimension Reduction (Variable Selection in Nonparametric Regression, Nonparametric Link Function, Semi- or Nonparametric Index)
2. Generalized Linear Model (Exponential Family, Link Function)
May 22
1. Single Index Model
2. Estimation (Semi-parametric Least Square, Pseudo Likelihood Estimation, Weighted Average Derivative Estimation)
May 31
1. Partial Linear Model
2. Generalized Partial Linear Model
3. Estimation Algorithm for PLM & GPLM
June 5
1. Profile likelihood
2. Testing the GPLM (LRT, Modified LRT)
June 12
1. Additive Models
2. Generalized Additive Models

Mar. 27
1. ex1_05.pdf
  
  —-deadline: Apr.10
2. ex2_05.pdf; ex3_05.pdf; exercise in class($E(\epsilon’ A \epsilon)=?$)
  
  —-deadline: Apr.17
Apr. 3
1. Prove that $\hat{\beta}$ and SSE are independent.
2. What is R square?
Apr. 10
1. Why does the logit model choose the link function $G(\cdot)=\frac{1}{\exp (-X^T\beta)}$ ?
Apr. 17
1. Exercise 3.1, 3.9, 3.14, Page 109 of “Nonparametric and Semiparametric__ Models-An introduction.pdf” ******
  
  —-deadline: May. 8**

June 26

Late homework has influence on the grade. The reduced points are in direct proportion to the time delayed.