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Smoothing and Nonparametric Regression

ETH Web: Smoothing and Nonparametric Regression

4 KP: Autumn Semester 2011 ETH (Main Building, HG E 21, Thursdays 10-12)

In this course, you will learn about the basic principles, methodological aspects and some of the basic computational issues of smoothing and nonparametric regression. In order to understand how the methods work, we will consider some examples from environmental and natural sciences. Note however that the statistical issues that we will address here are fairly general and can be broadly applied to many other types of data. Thus what you learn here will also have applications in various other fields of science.

Language of instruction: English
First lecture: 22.09.2011
Last lecture: 22.12.2011

ETH Academic Calendar

Prerequisites

Linear Algebra, Calculus, Introductory Statistics and Probability (e.g. 401-0624-00 G - Mathematik IV) including basics of Statistical Inference (Estimation & Testing).

Software: Working knowledge of R or S-Plus can be convenient, although not absolutely necessary to join the course. You can learn about using these software from books (for references click here) and a short note on some basic commands (to be posted at this site).

Visit this page for some relevant information (source: Seminar for Statistics, ETH Zürich).

Rough Outline

Revision of basic material
Regression & diagnostics
Smoothing and nonparametric regression
Density estimation, Kernel regression, Local polynomials, Smoothing splines, Bandwidth selection methods
Applications: selected examples

Some Text Books

Link to NEBIS

Books on Smoothing: Additional references to books & papers will be given out in the lectures.

Density Estimation, by B.W. Silverman, Chapman and Hall.
Kernel Smoothing, by M.P. Wand and M.C. Jones, Chapman and Hall.
Nonparametric Simple Regression, by J. Fox, Sage Publications.
Applied Smoothing Techniques for Data Analysis: the Kernel Approach With S-Plus Illustrations, by A.W. Bowman, A. Azzalini, Oxford University Press.

An additional list of text books (click on the titles):

Statistical inference
Regression
The S language (relevant for R or S-plus)

Final Exam

Oral exam (language: English) at the end of the semester. This will be a closed books & closed notes exam.

Some sample problems for practice

Lecture notes

__________________________________________________________________________________________________
Note: As mentioned earlier, these notes are not complete. Follow your in-class lecture notes for preparing for the exam.
__________________________________________________________________________________________________

Short summaries of lecture notes can be found <<here.*>> This site is under construction. *To login, use your user-id and password for this course.

Contents (posted so far)

Basic notations and terminologies
Simple linear regression
Multiple regression
Density estimation (a) Nonparametric kernel density estimation - Part I: Bias, Variance, Optimum bandwidth; (b) Comparison: MLE vs. nonparametric method; (c) A simple R-code & its output; (d) Nonparametric kernel density estimation - Part II: Likelihood cross-validation, Least square cross-validation, .. (e) Some computational exercises (not for handing in);

Last update 09.11.2011; ~ 2:00 pm;

.. to be continued.

(coming up ..)

Nonparametric Density Estimation:

(a) Efficiency of kernels (posted)

Nonparametric regression:

(a) Priestley-Chao Regression estimator when the x-values are fixed and evenly spaced: Leading terms in bias, variance and MSE and optimal bandwidth selection (posted in part 1), Least square Cross Validation (posted)
(b) Priestley-Chao Regression estimator when the x-values are unevenly spaced (random design): Bias, Variance etc. (posted with (c))
(c) Nadaraya-Watson estimator (random design) - general outline of how and why the method works (posted with (b))
(d) Local polynomials: Details of the estimator (posted in part 1), formula for confidence band (posted in part 1), rules for the choice of the degree of the polynomial (posted)
(e) Smoothing splines (posted; not part of the exam)

Feedback

For questions or comments, please send me an email at rita.ghosh@wsl.ch. I will get back to you with a reply as soon as possible.

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In order to understand how the methods work, we will consider some examples from environmental and natural sciences. Note however that the statistical issues that we will address here are fairly general and can be broadly applied to many other types of data. Thus what you learn here will also have applications in various other fields of science. Language of instruction: English First lecture: 22.09.2011 Last lecture: 22.12.2011 ETH Academic Calendar Prerequisites Linear Algebra, Calculus, Introductory Statistics and Probability (e.g. 401-0624-00 G - Mathematik IV) including basics of Statistical Inference (Estimation & Testing). Software: Working knowledge of R or S-Plus can be convenient, although not absolutely necessary to join the course. You can learn about using these software from books (for references click here) and a short note on some basic commands (to be posted at this site). Visit this page for some relevant information (source: Seminar for Statistics, ETH Zürich). Rough Outline Revision of basic material Regression & diagnostics Smoothing and nonparametric regression Density estimation, Kernel regression, Local polynomials, Smoothing splines, Bandwidth selection methods Applications: selected examples Some Text Books Link to NEBIS Books on Smoothing: Additional references to books & papers will be given out in the lectures. Density Estimation, by B.W. Silverman, Chapman and Hall. Kernel Smoothing, by M.P. Wand and M.C. Jones, Chapman and Hall. Nonparametric Simple Regression, by J. Fox, Sage Publications. Applied Smoothing Techniques for Data Analysis: the Kernel Approach With S-Plus Illustrations, by A.W. Bowman, A. Azzalini, Oxford University Press. An additional list of text books (click on the titles): Statistical inference Regression The S language (relevant for R or S-plus) Final Exam Oral exam (language: English) at the end of the semester. This will be a closed books & closed notes exam. *Some sample problems for practice* Lecture notes __________________________________________________________________________________________________ Note: As mentioned earlier, these notes are not complete. Follow your in-class lecture notes for preparing for the exam. __________________________________________________________________________________________________ Short summaries of lecture notes can be found <<here.>> This site is under construction. To login, use your user-id and password for this course. Contents (posted so far) Basic notations and terminologies Simple linear regression Multiple regression Density estimation (a) Nonparametric kernel density estimation - Part I: Bias, Variance, Optimum bandwidth; (b) Comparison: MLE vs. nonparametric method; (c) A simple R-code & its output; (d) Nonparametric kernel density estimation - Part II: Likelihood cross-validation, Least square cross-validation, .. (e) Some computational exercises (not for handing in); Last update 09.11.2011; ~ 2:00 pm; .. to be continued. (coming up ..) Nonparametric Density Estimation: (a) Efficiency of kernels (posted) Nonparametric regression: (a) Priestley-Chao Regression estimator when the x-values are fixed and evenly spaced: Leading terms in bias, variance and MSE and optimal bandwidth selection (posted in part 1), Least square Cross Validation (posted) (b) Priestley-Chao Regression estimator when the x-values are unevenly spaced (random design): Bias, Variance etc. (posted with (c)) (c) Nadaraya-Watson estimator (random design) - general outline of how and why the method works (posted with (b)) (d) Local polynomials: Details of the estimator (posted in part 1), formula for confidence band (posted in part 1), rules for the choice of the degree of the polynomial (posted) (e) Smoothing splines (posted; not part of the exam) Feedback For questions or comments, please send me an email at rita.ghosh@wsl.ch. I will get back to you with a reply as soon as possible.