Applied Nonparametric and Modern Statistics

• The class outline. For each section, you can obtain the class notes in pdf, the latex files for each section, and the R (or S-Plus) code used to generate the analyses and graphs. You can use this R code to generate the graphs used in the latex documents or download the compressed tar file and get them from the Plots directory.
• Links for homework : data needed, assignments sheets in pdf, and the latex files.
• Books often referenced
• Computing resource.
• Class general information.

1. Introduction [PDF, LaTeX]
2. Overview of various smoothers [PDF, LaTeX, R-code]
   1. Parametric smoothers [LaTeX]
   2. Bin smoothers [LaTeX]
   3. Running mean/moving average smoothers [LaTeX]
   4. Kernel smoothers and some asymtotic results [LaTeX]
   5. Linear Smoother [LaTeX]
3. Local Regression [PDF, LaTeX, R-code]
   1. Bibliography [LaTeX]
4. Splines [PDF, LaTeX, R-code]
   1. Linear Spaces (Parametric vs. Nonparametric) [LaTeX]
   2. Local Polynomials [LaTeX]
   3. Splines [LaTeX]
   4. Natural Smoothing Splines [LaTeX]
   5. Bibliography [LaTeX]
5. Resampling methods: Bias, Variance, and their trade-off [PDF, LaTeX, R-code]
   1. Bias-Variance Trade-off [LaTeX]
   2. Cross Validation: Choosing smoothness parameters [LaTeX]
   3. Bootstrap Standard Errors and Confidence Sets [LaTeX]
6. Connections [PDF, LaTeX, R-code, Splus5-code]
   1. Linear Smoothers: Influence, Variance, and Degrees of Freedom [LaTeX]
   2. Smoothing and Penalized Least Squares [LaTeX]
   3. Eigen analysis and spectral smoothing [LaTeX]
   4. Economical Bases: Wavelets and REACT estimators [LaTeX]
   5. Bayesian Model for Cubic Splines [LaTeX]
   6. Mixed Models and Splines [LaTeX]
7. High Dimensional Problems [PDF, LaTeX, Splus5-code]
   1. Projection Pursuit [LaTeX]
   2. Additive Models [LaTeX]
   3. Classification and Regression Tress (CART) [LaTeX]
      (guest lecturer: Ingo) [Data, code]
8. Generalized Models [PDF, LaTeX, Splus5-code]
   1. Generalized Additive Models (GAM) [LaTeX]
   2. Local Likelihood [LaTeX]
9. Model Selection [PDF LaTeX]
   1. Mallow's Cp [LaTeX]
   2. Information Criteria (e.g. AIC) [LaTeX]
   3. Posterior Probability Criteria (e.g. BIC) [LaTeX]
10. Introduction to Time Series Analysis [PDF, LaTeX]
    1. Stationarity
    2. Auto-correlation function
    3. Spectral analysis

Sample LaTeX document

• Homework 1 [PDF, LaTeX]: Paper refered to by first hint.
• Homework 2 [PDF, LaTeX]
• Homework 3 [PDF, LaTeX]

Data-sets:

• CD4 cell count example
• Sr data set
• Intensities data
• Gene expression microarray data
• Diabetes study data
• Kyphosis study data

• R, S-Plus, or MATLAB.
• LaTex
• Emcas (recomended)

• Official course title: Advanced Generalized Linear Models IV 140.753-754
• Unofficial title: Applied Nonparametric and Modern Statistics
• Even less official title: GAM class
• Instructor: Rafael A. Irizarry
• Office hours by appointment, Room: E2008
• Phone 410-614-5157, email: rafa@jhu.edu
• No Required book!
• I assume you know: Linear Algebra (651--654 level), Statitical theory (771--772 level), and GLM (751-753 level).
• You are required to use one of the following computer packages: R (recommended), S-Plus, or MATLAB.
• You are required to type up your homework in LaTeX
• Grading: 4 homeworks 60%, 1 applied project 20%, Presentation of project (in-class presentation) 20%.