STA 586 NONPARAMETRIC CURVE ESTIMATION


Department of Mathematics and Statistics, UNM


Fall Semester 2003


INSTRUCTOR

Dr. Gabriel Huerta
Office: 441 Humanities Building
email: ghuerta@stat.unm.edu
Class Time: Tue. and Thurs. 2:00-3:15.
Classroom: 126 Dane Smith Hall
Course Web-Page: http://www.stat.unm.edu/~ghuerta/nonpar/course.html
Office Hours: Mon and Wed. 10:00-11:30 or by appointment.
*Please send me a note by e-mail to make an appointment outside office hours.


DESCRIPTION

This course is concerned with estimation of nonparametric curves including probability density functions, nonparametric regression models, time series analysis and signal filtering. Different statistical methods will be presented including orthogonal series, kernels, splines and wavelets. Whenever possible, distinctions will be made between different statistical approaches to these methods, including issues about Frequentist vs. Bayesian. The focus of the course will be applied rather than theoretical. The methods will be illustrated with different data examples using S-plus. The goal of the course is that the students gain a good understanding and make good applications of modern non-parametric methods in their own research areas.

PREREQUISITES

STA 453/553: Statistical Inference or permision of the instructor

In order to have a complete understading of this course, you must familiar with the main concepts of statistical inference for parametric models including, families of distribution functions, likelihood, point estimation and interval estimation. Appendix A reviews some of the fundamentals in these topics. In fact, the first homework assignment is that you read Appendix A and work with exercises A.5, A.7, A.12, A.14, A.18. Due Thursday, September 4th.

TEXTBOOK

  • Efromovich, S. (1999)Nonparametric Curve Estimation: Methods, Theory and Applications; Springer Verlag: New York

    • This book is required and please bring it to class since we will follow it very closely.

    ADDITIONAL TEXT

  • Vidakovic, B. (1999) Statistical Modeling by Wavelts Wiley.

    • This book is only recommended for the course. Its main use will be to complement the material on Wavelets presented by Efromovich. Particularly, this book has a complete chapter on Bayesian Methods in Wavelets.


    HOMEWORK

    Here, I will post homework assignments and computer exercises (starting from HW2).


    TOPICS

  • Chapter 1: Introduction to nonparametric curve estimation. Chapter 2: Orthogonal series approximation .
  • Chapter 3: Density estimation.
  • Chapter 4: Regression.
  • Chapter 5: Time Series.
  • Chapter 6: Multivariate functions.
  • Chapter 7: Filtering signals.
    • GRADING

    The grading will be based on homework assignments, computer exercises, a 'take home' final and class participations. Homeworks will be assigned regularly and mainly, they will consist of exercises taken out of the textbook. Computer exercises refer to the Practical Seminars in the book. The final will consist of a set of exercises, theoretical and practical to review all the topics covered in class.

    SOFTWARE

    Mainly, we will use Sam Efromovich's Splus functions which are companion to the textbook. Here is a link to the files that contain the functions . For installation, read Appendix B and the file news.INSTALLATION. If you questions, please let me know.

    Also, Brani Vidakovic has some Splus software for his Wavelet book and we might use this software every now and then. Here is a link to the website of the book which includes a link to the software. In order to use these functions, you only need to know basic Splus commands.

    However, if you are not familiar at all with Splus, here is some documentation with many examples of how to perform statistical analysis using Splus.