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Course, academic year 2023/2024
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Mathematical Statistics 4 - NMST545
Title: Matematická statistika 4
Guaranteed by: Department of Probability and Mathematical Statistics (32-KPMS)
Faculty: Faculty of Mathematics and Physics
Actual: from 2023
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: English, Czech
Teaching methods: full-time
Teaching methods: full-time
Guarantor: Mgr. Stanislav Nagy, Ph.D.
doc. Ing. Marek Omelka, Ph.D.
Class: M Mgr. PMSE
M Mgr. PMSE > Povinně volitelné
Classification: Mathematics > Probability and Statistics
Co-requisite : {At least one courses in linear regression models}
Incompatibility : NMST434
Annotation -
Last update: doc. Ing. Marek Omelka, Ph.D. (30.11.2020)
Bootstrap and nonparametric kernel smoothing methods
Aim of the course -
Last update: doc. Ing. Marek Omelka, Ph.D. (02.12.2020)

To understand principles of bootstrap and kernel smooghting methods.

Course completion requirements -
Last update: doc. Ing. Marek Omelka, Ph.D. (02.12.2020)

Oral exam. As a part of the exam the students will hand in a solution to homeworks assigned during the semester.

Literature -
Last update: doc. Ing. Marek Omelka, Ph.D. (02.12.2020)

FAN, J. and GIJBELS, I.: Local Polynomial Modelling and Its Applications. Chapman & Hall/CRC, London, 1996

WAND, M. P. and JONES, M. C.: Kernel Smoothing. Chapman & Hall, 1995

SHAO, J. and TU, D.: The jackknife and bootstrap. Springer, New York, 1996.

Teaching methods -
Last update: doc. Ing. Marek Omelka, Ph.D. (02.12.2020)


Requirements to the exam -
Last update: doc. Ing. Marek Omelka, Ph.D. (30.11.2020)

The exam will be organized as follows. First, an example will be given and there will be about 50 minutes to solve this example. After handing in this example, the student can make a short break, after which he/she gets two theoretical questions. To pass the exam, the student has to prove that he/she can solve the example as well as answer the theoretical questions in a satisfactory way.

The requirements for the oral exam are in agreement with the syllabus of the course as presented during lectures.

Syllabus -
Last update: doc. Ing. Marek Omelka, Ph.D. (03.12.2020)


Kernel density estimation,

Kernel nonparametric regression.

Entry requirements -
Last update: doc. Ing. Marek Omelka, Ph.D. (30.11.2020)

It is assumed that the students have already a very solid knowledge of statistics and probability theory.

This is covered for instance by

Mukhopadhyay, N. (2000). Probability and statistical inference. CRC Press - almost the whole book except for Chapters 10 and 13

Khuri, A. I. (2009). Linear model methodology. Chapman and Hall/CRC - the knowledge of Chapters 1 - 6 is sufficient.

The students are prepared for the course if they pass the following courses:

Mathematical Statistics 1 and 2 (NMSA331 and NMSA332),

Probability Theory 1 (NMSA333),

Linear regression (NMSA407).

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