# 401-0627-00L Smoothing and Nonparametric Regression with Examples

Semester | Autumn Semester 2018 |

Lecturers | S. Beran-Ghosh |

Periodicity | yearly recurring course |

Language of instruction | English |

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. Examples from environmental research will be used for motivation, but the 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 Maximum likelihood, Method of Least squares: regression & diagnostics - Nonparametric curve estimation o Density estimation, Kernel regression, Local polynomials, Bandwidth selection o Selection of special topics (as time permits, we will cover as many topics as possible) such as rapid change points, mode estimation, robust smoothing, partial linear models, etc. - Applications: potential areas of applications will be discussed such as, change assessment, trend and surface estimation, probability and quantile curve estimation, and others. |

Lecture notes | Brief summaries or outlines of some of the lecture material will be posted at https://www.wsl.ch/en/employees/ghosh.html. NOTE: The posted notes will tend to be just sketches whereas only the in-class lessons will contain complete information. LOG IN: In order to have access to the posted notes, you will need the course user id & the password. These will be given out on the first day of the lectures. |

Literature | References: - 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. - Kernel Smoothing, by M.P. Wand and M.C. Jones, Chapman and Hall. - Local polynomial modelling and its applications, by J. Fan and I. Gijbels, Chapman & 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. - Kernel Smoothing: Principles, Methods and Applications, by S. Ghosh, Wiley. Additional references will be given out in the lectures. |

Prerequisites / Notice | Prerequisites: A background in Linear Algebra, Calculus, Probability & Statistical Inference including Estimation and Testing. |