||6 credit points
||Castro, R.M. (Technische Universiteit Eindhoven)
||The aim of this course it to obtain a broad knowledge of nonparametric methods in statistics. Many methods in statistics are parametric in nature. In this case the underlying probability law of the data is assumed to be parametrized by a finite-dimensional parameter. The basic idea of nonparametric methods is to drop this often restrictive assumption. These methods thereby offer much more flexibility to model the data than classical parametric methods. The topics that we will cover in this course form a mix of classical distribution free methods, like goodness-of-fit tests and rank-based methods, and more modern topics in non-parametric regression and density estimation. The focus includes both the development and formal analysis of some of the methods, as well as their application and practical considerations. Examples will be illustrated using the statistical computing tools, namely the statistical computing package R.
||The first 5 to 6 weeks will be devoted to the following topics:
• Introduction to nonparametric inference and the empirical distribution function • Goodness of fit tests • Permutation tests • Rank testsWeeks 7 up till 13 will be used to cover various topics in non-parametric statistics, which include smoothing and nonparametric regression.
||Each class consists roughly of three 45 minutes time slots. The third hour will be used for discussion of course materials and exercises (essentially "office hours").
Throughout the course you will be required to solve some homework exercises. Some of these will be theoretical, while others will be practical, and often require the use of computational tools. It is recommended that you use the statistical computing package R for these, but this is not mandatory, and you can use any other software you have access to and feel comfortable with. The homework exercises that are handed in in a timely fashion will be graded and provide extra credit points towards the final grade. At the end of the course there is a final written examination.
||The homework exercises that are handed in in a timely fashion will be graded and provide extra credit points towards the final grade. At the end of the course there is a final written examination.
||The contents of the course will be taken from various sources, which include lecture notes. A part of the course will follow closely some chapters of the book "All of Nonparametric Statistics" (Springer; author: L. Wasserman, "ISBN-10:" 0387251456). However, having this book is not mandatory.
||Basic knowledge of probability and statistics, and the level of mathematical maturity expected of a master student in mathematics, engineering or statistics.