## M8113 Theory and Practice of Kernel Smoothing

Faculty of Science
Spring 2022
Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Taught in person.
Teacher(s)
prof. RNDr. Ivanka Horová, CSc. (lecturer)
doc. Mgr. Jan Koláček, Ph.D. (seminar tutor)
Guaranteed by
doc. Mgr. Jan Koláček, Ph.D.
Department of Mathematics and Statistics - Departments - Faculty of Science
Supplier department: Department of Mathematics and Statistics - Departments - Faculty of Science
Prerequisites
Basic knowledge of probability and mathematical statistics
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The theory and methods of smoothing have been developed mainly in the last years. The existence of high speed inexpensive computing has made it easy to look at the data in ways that were once impossible. The power of computer now allows great freedom in deciding where an analysis of data should go. One area that has benefited greatly from this new freedom is that of nonparametric density, distribution, and regression function estimation,or what are generally called smoothing methods. This subject aims to give a survey of modern nonparametric methods of a density a distribution function, a regression function and bivariate density estimates.
Learning outcomes
Student will be able:
- to analyze a given set of real dat;
- to propose a suitable method for data processing;
- to give implementation and create computer programs;
Syllabus
• Basic idea of smoothing.
• General principle of kernel estimates.
• Kernel estimates of a density, criterion for quality of estimates, problem of a choice of a bandwidth, canonical kernels and optimal kernel theory, kernels of higher orders.
• Kernel estimates of a distribution function, a choice of a bandwidth.
• Various types of kernel estimates of regression functions, comparision of these estimates, boundary effects problem, criterion for a quality of estimates.
• The presented theory is followed by practical examples. All presented method are implemented in Matlab.The toolbox is available on http://www.math.muni.cz/veda-a-vyzkum/vyvijeny-software/274-matlab-toolbox.html
Literature
recommended literature
• WAND, M. P. and M. C. JONES. Kernel smoothing. 1st ed. London: Chapman & Hall, 1995. 212 s. ISBN 0412552701. info
• SILVERMAN, B. W. Density estimation for statistics and data analysis. 1st ed. Boca Raton: Chapman & Hall, 1986. ix, 175. ISBN 0412246201. info
• Smoothing and regression : approaches, computation, and application. Edited by Michael G. Schimek. New York: John Wiley & Sons, 2000. xix, 607. ISBN 0471179469. info
• SIMONOFF, Jeffrey S. Smoothing methods in statistics. New York: Springer-Verlag, 1996. xii, 338. ISBN 0387947167. info
• Statistical theory and computational aspects of smoothing :proceedings of the COMPSTAT '94 satellite meeting held in Semmering, Austria 27-28 August 1994. Edited by Wolfgang Härdle - Michael G. Schimek. Heidelberg: Physica-Verlag, 1996. viii, 265. ISBN 3-7908-0930-6. info
• HOROVÁ, Ivanka, Jan KOLÁČEK and Jiří ZELINKA. Kernel Smoothing in MATLAB: Theory and Practice of Kernel Smoothing. Singapore: World Scientific Publishing Co. Pte. Ltd., 2012. 244 pp. ISBN 978-981-4405-48-5. URL info
Teaching methods
Lecture: 2 hours weekly Class excercise: 1 hour weekly. The excercise is aimed at application of methods delivered in the lecture including the use of the toolbox
Assessment methods
Lecture.Compulsory attendance of excercises. Oral exam.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
General note: Jedná se o inovovaný předmět Neparametrické vyhlazování.
Teacher's information
The lessons are usually in Czech or in English as needed, and the relevant terminology is always given with English equivalents.

The target skills of the study include the ability to use the English language passively and actively in their own expertise and also in potential areas of application of mathematics.

Assessment in all cases may be in Czech and English, at the student's choice.

The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021.
• Enrolment Statistics (Spring 2022, recent)