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 2015 to 2017
• Semester: summer
• E-Credits: 8
• Hours per week, examination: summer s.:4/2, C+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: doc. Ing. Marek Omelka, Ph.D.
• Class: M Mgr. PMSE; M Mgr. PMSE > Povinně volitelné
• Classification: Mathematics > Probability and Statistics
• Pre-requisite : NMSA407
• Is pre-requisite for: NMST533

Annotation

English

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.

Czech

Last update: T_KPMS (16.05.2013)

Moderní metody statické inference založené na teorii maximální věrohodnosti a jejich zobecněních. Základy neparametrických a robustních metod. Metody pro data s chybějícími pozorováními.

Aim of the course

English

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

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

Czech

Last update: T_KPMS (16.05.2013)

Studenti se seznámí s principy pokročilých metod statistické inference, na kterých jsou postaveny metody analýzy dat.

Literature

English

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.

Czech

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

ANDĚL, J.: Základy matematické statistiky. Matfyzpress, Praha, 2007.

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.

Doplňující literatura:

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

English

Last update: T_KPMS (16.05.2013)

Lecture+exercises.

Czech

Last update: T_KPMS (16.05.2013)

Přednáška+cvičení.

Syllabus

English

Last update: doc. Ing. Marek Omelka, Ph.D. (22.02.2018)

Clipping from the asymptotic theory - Delta Theorem

Theory of maximum likelihood

Profile, conditional and marginal likelihood

M-estimators and Z-estimators

Quasi-likelihood

Quantile regression

Kernel density estimation

Kernel nonparametric regression

Bootstrap

EM-algorithm

Methods for missing data

Czech

Last update: doc. Ing. Marek Omelka, Ph.D. (16.02.2018)

Asymptotické metody - Delta věta

M-odhad a Z-odhady

Teorie maximální věrohodnosti

Kvazivěrohodnost, profilová, podmíněná a marginální věrohodnost

Kvantilová regrese

Jádrové odhady hustot

Jádrová neparametrická regrese

Bootstrap

Metody pro chybějící data

EM-algoritmus