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:

• Part 1 —- Linear Models Searle, S. R. Linear Models

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

Outline:

• 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. 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)
• 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

Homework:

• 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(⋅)=1exp(−XTβ)G(⋅)=1exp⁡(−XTβ) ?

• Apr. 17

  1. Exercise 3.1, 3.9, 3.14,  Page 109 of “Nonparametric and Semiparametric__ Models-An introduction.pdf” ******

     —-deadline: May. 8**

Final Exam:

June 26

Grading Policy:

• 20% homework
• 50% final exam
• 30% paperwork

Note:

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

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