25.3.2015

Pozývame Vás na seminár z matematickej štatistiky, s názvom "Regression quantiles and their application in the optimal threshold selection in a POT model", ktorý sa uskutoční v stredu, 4. mája 2015, o 9:50 na Seminári FMFI UK v Bratislave (miestnosť XII FMFI UK). Prednášať bude Mgr. Martin Schindler Ph.D. (Katedra aplikované matematiky, Fakulta přírodovědně-humanitní a pedagogická, Technická univerzita v Liberci).

Regression quantiles and their application in the optimal threshold selection in a POT model

Martin Schindler

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.