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Smoothing and Nonparametric Regression with Examples
Last Updated: 2026-02-05 16:29:34
Abstract
Starting with an overview of selected results from parametric inference, kernel smoothing will be introduced along with some asymptotic theory, optimal bandwidth selection, data driven algorithms and some special topics. Selected numerical examples will be used for motivation. The presented methods will also be applicable elsewhere.
Objective
The students will learn about methods of kernel smoothing and application of concepts to data. The aim will be to build sufficient interest in the topic and intuition as well as the ability to implement the methods to various different datasets.
Content
Rough Outline: - Parametric estimation methods: selection of important results o Method of Least squares: regression & diagnostics - Nonparametric curve estimation o Density estimation, Kernel regression, Local polynomials, Bandwidth selection, various theoretical results related to consistency o Selection of special topics (as time permits, we will discuss some of the following): rapid change points, mode estimation, partial linear models, probability and quantile curve estimation, etc. - Applications: potential areas of applications will be discussed such as, change assessment, trend and surface estimation and others.
Resources
Lecture Notes
Summaries or outlines of some of the lecture material may be communicated to registered students by Email at irregular intervals.Note: These summaries/outlines will tend to be brief, likely to be incomplete & may have typos. Only in-class lessons will contain complete information.
Literature
References: - Kernel Smoothing: Principles, Methods and Applications, by Sucharita Ghosh, Wiley. - Statistical Inference, by S.D. Silvey, Chapman & Hall. - Regression Analysis: Theory, Methods and Applications, by A. Sen and M. Srivastava, Springer. - Density Estimation, by B.W. Silverman, 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. Additional references will be given out in the lectures.
Learning Materials (Links)
General Information
- Language
- English
- Levels
- MSC
- Frequency
- Yearly recurring
Examination
- Type
- session examination
- Mode
- oral 30 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture with exercise | Smoothing and Nonparametric Regression with Examples |
|
2 h weekly |
Offered In
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Statistics Master (The following courses belong to the curriculum of the Master's Programme in Statistics. The corresponding credits do not count as external credits even for course units where an enrolment at ETH Zurich is not possible.)