Předmět Advanced Statistics (JEB035)

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Materiál	Typ	Datum	Počet stažení

Cíl

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.

Sylabus

I. Bayesian statisticsBasic idea of bayesian statistics, Bayes´ theorem, systems of apriori- distributions, uncertainty principal, Jeffrey´s theoremand corresponding system of apriori-distributions.Predictive density. Types of estimates.II. Tests of good fitChi-squre test of good fit with known and unknown parameters.Kolmogorov-Smirnovov´s tests. Tests of good fit for some special distributions.III. Contingency tablesTest of independence and of symmetry, Fisher´s and McNemara´s tests. Stuart´s test. Simpson paradox.IV. Sampling from finite populationsBasic 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.

Literatura

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 Inferenceand Time Series Analysis:  Festschrift for Jana Jureckova, Vol. 7(2010), 254 - 267. DOI: 10.1214/10 - IMSCOLL725 ISBN978-0-940600-80-5, ISSN 1939-4039 (and my papers given there as references).

Požadavky

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

Garant

prof. RNDr. Jan Ámos Víšek, CSc.

Vyučující

PhDr. RNDr. Josef Stráský, Ph.D.prof. RNDr. Jan Ámos Víšek, CSc.