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25.3.2015
We invite you to the mathematical statistics seminar "Regression quantiles and their application in the optimal threshold selection in a POT model". The Seminar will take place on May 4, 2015, 9:50 on Seminar FMPHI CU in Bratislava (room XII FMPHI CU). Mgr. Martin Schindler Ph.D. (Department of Applied Mathematics, Faculty of Science, Humanities and Education, Technical University in Liberec, Czech Republici) will present a talk.
Regression quantiles and their application in the optimal threshold selection in a POT model
Martin Schindler
Technical University of Liberec
Univerzitní náměstí 1410/1, 461 17 Liberec 1, Czech Republic
E-mail:
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In the first part the regression quantiles and
regression rank scores, as natural extensions of ordinary quantiles and
ranks, are introduced. Both linear and nonlinear regression quantiles
and rank scores are considered. Computational problems in the nonlinear
models are mentioned and a method how to work them out is proposed and
applied to real data.
Next, the peaks-over-threshold (POT) method with a
non-stationary threshold for estimating high quantiles is investigated.
It was shown that using (95%) regression quantile as the time-dependent
threshold instead of a constant treshold can beneficial. It is assumed
that a linear trend is present in the data and so a linear regression
quantile as the threshold is used. The aim is to find the threshold
(regression quantile) which would be optimal with respect to the
reliability of the estimates of high quantiles by means of Monte Carlo
simulations. Based on this criterion stationary and regression quantile
thresholds are compared. It is described how the choice of the optimal
threshold depends on the sample size, estimated quantile or the estimate
itself.
Keywords: Regression quantiles, Nonlinear regression, Peak Over Threshold, Return level.
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