M8113 Nonparametric Smoothing

Faculty of Science
Spring 2008 - for the purpose of the accreditation
Extent and Intensity
2/1. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ivanka Horová, CSc. (lecturer)
Mgr. Jiří Zelinka, Dr. (seminar tutor)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Ivanka Horová, CSc.
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 as kernel estimates of univariate and multivariate densities, and kernel estimates of regression functions as well.The smoothing splines are also dealt with.
Syllabus
  • Basic idea of smoothing. General principle of kernel estimates. Kernel estimates of univariate and multivariate densities,criterion for quality of estimates,problem of a choice of a bandwidth,,canonical kernels and optimal kernel theory,kernels of higher orders. Various types of kernel estimates of regression functions,comparision of these estimates,boundary effects problem,criterion for a quality of estimates. Smoothing splines,shape preserving splines. The theory presented at the lecture is followed by practical examples .
Literature
  • SIMONOFF, Jeffrey S. Smoothing methods in statistics. New York: Springer-Verlag, 1996, xii, 338. ISBN 0387947167. info
  • SILVERMAN, B. W. Density estimation for statistics and data analysis. 1st ed. Boca Raton: Chapman & Hall, 1986, ix, 175. ISBN 0412246201. info
  • WAND, M. P. and M. C. JONES. Kernel smoothing. 1st ed. London: Chapman & Hall, 1995, 212 s. ISBN 0412552701. 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
Assessment methods (in Czech)
Přednáška, cvičení v počiačové učebně. Zkouška :ústní
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms 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, Spring 2022, Spring 2023, Spring 2024, Spring 2025.