Advanced Statistics - JEB035

• Title: Advanced Statistics
• Guaranteed by: Institute of Economic Studies (23-IES)
• Faculty: Faculty of Social Sciences
• Actual: from 2016 to 2017
• Semester: winter
• E-Credits: 6
• Examination process: winter s.:
• Hours per week, examination: winter s.:2/2, Ex [HT]
• Capacity: 59 / 34 (59)
• Min. number of students: unlimited
• 4EU+: no
• Virtual mobility / capacity: no
• State of the course: taught
• Language: English
• Teaching methods: full-time
• Teaching methods: full-time
• Note: course can be enrolled in outside the study plan; enabled for web enrollment; priority enrollment if the course is part of the study plan
• Guarantor: prof. RNDr. Jan Ámos Víšek, CSc.
• Teacher(s): Mgr. Tomáš Křehlík, Ph.D.; prof. RNDr. Jan Ámos Víšek, CSc.
• Pre-requisite : JEB105

Annotation

Last update: VISEK (01.10.2012)

The course is a continuation of the courses Probability and mathematical statistics and Econometric I and it larges knowledge from there about the new topics, namely frequently used ones. Firstly, the attention is paid to the bayesian statistics, i.e. to the possibility to utilize the a priori obtained knowledge in the statistical inference. It is an approach which is alternative to the classical Fisher statistics. Then we shall turn to the tests of good fit, processing of contingency tables, theory of selection from finite populations and finally we will study robustness which the most problematic aspects of classical statistical and econometric methods.

Aim of the course

Last update: VISEK (01.10.2012)

To enlarge knowledge in statistics and econometrics about some selected topics. To help in this way to the understanding of basic statistical and econometric ideas.

Literature

Last update: VISEK (01.10.2012)

Breiman, L. (1968): Probability, Addison-Wesley Publishing Company, London 1968.                                                                                                                                                                                           

Hampel, F. R., E. M. Ronchetti, P. J. Rousseeuw, W. A. Stahel  (1986):  Robust  Statistics -- The Approach Based on Influence Functions. New York: J.Wiley                                                                                                                                                                                                                                                                                                           

Huber, P.J.(1981):  Robust Statistics. New York: J.Wiley and Sons.

Lehmann, E. L. (1998): Theory of Point Estimation (Springer Texts in Statistics)

Lehmann, E. L. (1998): Testing Statistical Hypotheses, (Springer Texts in Statistics).

Rao, R. C. (1973): Linear Statistical Inference and Its Applications. New York: J.Wiley and Sons.                                                                                                                                                                                                                                                                                                                      

Rousseeuw, P. J., A. M. Leroy (1987):  Robust Regression and Outlier Detection.  New York: J.Wiley and Sons.

Víšek, J. Á. : Selected Topics from Statistics. Carolinum.                                                                                                                                                                                                                                       

Víšek, J. Á. : Robust error-term-scale estimate. IMS Collections. Nonparametrics and Robustness in Modern Statistical Inference
and Time Series Analysis:  Festschrift for Jana Jureckova, Vol. 7(2010), 254 - 267. DOI: 10.1214/10 - IMSCOLL725 ISBN
978-0-940600-80-5, ISSN 1939-4039 (and my papers given there as references).

Teaching methods

Last update: VISEK (01.10.2012)

Lectures with seminars. All relevant information will be available on my IES web page, i.e. http://ies.fsv.cuni.cz/cs/staff/visek

Requirements to the exam

Last update: VISEK (01.10.2012)

Writing reports - homeworks from seminars and passing tests for credits.

Syllabus

Last update: VISEK (01.10.2012)

I. Bayesian statistics
Basic idea of bayesian statistics, Bayes´ theorem, systems of apriori- distributions, uncertainty principal, Jeffrey´s theorem
and corresponding system of apriori-distributions.
Predictive density. Types of estimates.

II. Tests of good fit
Chi-squre test of good fit with known and unknown parameters.
Kolmogorov-Smirnovov´s tests. Tests of good fit for some special distributions.

III. Contingency tables
Test of independence and of symmetry, Fisher´s and McNemara´s tests. Stuart´s test. Simpson paradox.

IV. Sampling from finite populations
Basic idea, support of selection, probabilities of drawing and inclusion in the sample and their relations. Types of sampling
(simple random, Poisson´s, rejecting, Sampford´s, successive, stratified, more stages sampling), estimation of total.
Representativeness, unbiasedness. Basic ideas of questionnaries.                                                                                                                                                                                                                    

V. Repetition of the main ideas of and the reasons for robustness, the robust estimators of location and scale, the robust indetification                                                                                                                    of regression model, robustified diagnostics and modifications of the OLS. The implicit weighting of residuals.

Entry requirements

Last update: VISEK (01.10.2012)

Passing (some) mathematics, (some) statistics and (some) econometrics.