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J. Jaruskova - "Extreme Values" - Seminario - Cassino
Sperando di fare cosa gradita, invio invito per seminario venerd́ 16/4.
Cordiali saluti
Giovanni Porzio
UNIVERSITA' DEGLI STUDI DI CASSINO
DIPARTIMENTO ECONOMIA E TERRITORIO
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SEMINARIO
"EXTREME VALUE THEORY AND SOME APPLICATIONS"
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Prof. JANA JARUSKOVA
Department of Probability and Mathematical Statistics
Charles University of Prague
Venerd́' 16 aprile, ore 10:30-13:00 e 15:00-17:00, Aula 4
Facolta' di Economia
via Mazzaroppi snc, 03043 Cassino
Topics:
1.
Tail behavior of some estimators of location:
the sample mean and median, M and L estimators.
Tail behavior of the sample extremes.
Relation of the tail behavior and of the breakdown point of an estimator of
location.
2.
Tail behavior of estimators in the linear regression model.
Tail behavior of the least squares estimator and its relation to the hat
(projection) matrix:
the sample size either fixed or increasing, the regression matrix either fixed
or random.
3.
Pareto type distributions.
Estimators of the Pareto index: Pickands, Hill's and moment estimators.
Estimators based on the tail behavior of the sample mean.
4.
Extreme regression quantiles in the linear regression model, their asymptotic
behavior.
5.
Tests on the value of the Pareto index based on the subsample extremes, on the
subsample
averages and others.
Recommended literature:
1. Beirlant J., J. L. Teugels and P. Vynckier (1996).
Practical Analysis of Extreme Values. Leuven University Press.
2. Castillo E. (1988) Extreme Value Theory in Engineering. Academic Press.
3. Embrechts P., C. Kluppelberg and T. Mikosch (1997).
Modelling Extremal Events for Insurance and Finance. Springer-Verlag.
4. Jureckova J. (2003)
Statistical tests on tail index of a probability distribution (with a
discussion) METRON LXI/2, 151-190.
5. Kotz S. and S. Nadarajah (2000). Extreme Value Distributions. Theory and
Applications. Imperial College Press London (the 2nd Edition 2002).
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http://www.eco.unicas.it/strutture/mfa/statistica/
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