SubjectsSubjects(version: 873)
Course, academic year 2020/2021
Modern Statistical Methods - NMST434
Title: Moderní statistické metody
Guaranteed by: Department of Probability and Mathematical Statistics (32-KPMS)
Faculty: Faculty of Mathematics and Physics
Actual: from 2020
Semester: summer
E-Credits: 8
Hours per week, examination: summer s.:4/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: English, Czech
Teaching methods: full-time
Guarantor: doc. Ing. Marek Omelka, Ph.D.
Class: M Mgr. PMSE
M Mgr. PMSE > Povinně volitelné
Classification: Mathematics > Probability and Statistics
Pre-requisite : NMSA407
Annotation -
Last update: T_KPMS (16.05.2013)
Modern methods of statistical inference based on maximum likelihood theory and its generalizations. Fundamentals of nonparametric and robust methods. Methods for missing observations.
Aim of the course -
Last update: doc. Ing. Marek Omelka, Ph.D. (11.04.2018)

To understand principles of advanced methods of statistical inference that are used in data analysis.

Course completion requirements -
Last update: doc. Ing. Marek Omelka, Ph.D. (15.02.2019)

The exercise class credit is necessary to sign up for the exam.

To get the credit for the exercise class the student needs to get 100 points from the assigned homework tasks. During the semester a number of homework assignments will be given. It will be indicated how many points the student can get for each assignment. In total, it is possible to get 140 points (or a few more). Solutions to homework assignments have to be delivered at the beginning of the exercise class (usually there is one week to work on the problem). No points are given to the solutions that are delivered after the deadline.

To get the exercise class credit it is needed:

• to obtain at least 100 points in total; and

• to solve correctly the two indicated assignments.

Although in general one can skip some of the assignments, the two indicated assignments (bootstrap and EM algorithm) are compulsory. For the compulsory assignments, sending an R-code (that works) is required. In case that a compulsory assignment is not solved correctly, there will be exactly one possibility to improve/correct your solution. No additional points are given for the corrected version.

The nature of these requirements precludes any possibility of additional attempts to obtain the exercise class credit.

Literature -
Last update: doc. Ing. Marek Omelka, Ph.D. (11.04.2018)

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

LEHMANN, E. L. and CASSELLA, G. (1998). Theory of point estimation. Springer, New York.

MCLACHLAN, G. J., KRISHNAN, T.: The EM Algorithms and Extensions, Wiley, 2008

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.

Additional supporting literature:

KOENKER, R.: Quantile regression. Cambridge university press, 2005.

LITTLE, R.J.A., RUBIN, D.B.: Statistical analysis with missing data. New York: John Wiley & Sons, 1987

PAWITAN, Y.: In all likelihood: statistical modelling and inference using likelihood. Oxford University Press, 2001.

SERFLING, R. J.: Approximation Theorems of Mathematical Statistics, Wiley, 1980.

VAN DER VAART, A. W.: Asymptotic statistics. Cambridge university press, 2000.

Teaching methods -
Last update: T_KPMS (16.05.2013)


Requirements to the exam -
Last update: doc. Ing. Marek Omelka, Ph.D. (16.02.2019)

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. (11.04.2018)

Clippings from the asymptotic theory - Delta Theorem and Moment Estimators

Theory of maximum likelihood

Profile, conditional and marginal likelihood

M-estimators and Z-estimators

Robust estimation


Quantile regression


Methods for missing data

Kernel density estimation

Kernel nonparametric regression

Entry requirements -
Last update: doc. Ing. Marek Omelka, Ph.D. (24.05.2018)

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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