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Rekurzivní postupy pro detekci změny rozdělení
Chochola, Ondřej ; Černíková, Alena (oponent) ; Hušková, Marie (vedoucí práce)
In the thesis we study a sequential monitoring scheme for detecting a change in variance. We assume to have a stable historical period of length m. The goal is to propose tests with asymptotically small probability of type I error and power 1 as m tends to infinity. Two such procedures were proposed. The first uses estimates of variance from the historical period, the second uses recursive estimates. The distribution under the null hypothesis and also under the alternative hypothesis was derived for both test statistics. Furthermore a simulation study for of the finite sample performance of the monitoring schemes was conducted.
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Rekurzivní postupy pro detekci změny rozdělení
Chochola, Ondřej ; Hušková, Marie (vedoucí práce)
V předkládané práci studujeme otázku sekvenčního testování změny měřítka. Předpokládáme, že máme k dispozii stabilní historické období délky m. Cílem je odvodit testy s asymptoticky omezenou pravděpodobností chyby I. druhou a silou 1 při m jdoucím do nekonečna. Byly navrženy dvě takovéto procedury, první využívající odhadů rozptylu z histrického období a druhá odhadů rekurzivních. Pro obě testové statistiky byla odvozena rozdělení jak za platnosti nulové hypotézy, kdy se model nemění, tak i za platnosti alternativy, kdy v zenámém čase dojde ke změně měřítka. dále byla provedena simulační studie pro vyhodnocení výkonnosti procedur při konečném m.
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Tests for Multiple Changes in Linear Regression Models
Marušiaková, Miriam ; Hušková, Marie (vedoucí práce) ; Prášková, Zuzana (oponent) ; Picek, Jan (oponent)
We consider tests for multiple structural changes in linear regression models. The tests are based on F-type test statistics for the null hypothesis of no change against k changes or against an unknown number of changes with a given upper bound. We extend the existing results to linear regression models with deterministically trending regressors. Moreover, we introduce a generalized M-type test statistic which is based on functionals of weighted M-residuals. In change-point analysis approximations to critical values are usually obtained through the limit behavior of the respective test statistic under the null hypothesis. However, these approximations are often not satisfactory. Either the convergence of the test statistic to its limit distribution is rather slow or the limit distribution itself is very complex. An alternative approach is to apply resampling methods. We explore this possibility for F-type and M-type test statistics in the presence of multiple change points. We prove that the bootstrap method provides asymptotically correct critical values for the studied tests. We conduct several simulation experiments to show that the bootstrap based approximations are reasonable also in nite sample situations. Moreover, these approximations are often better than the asymptotic critical values. Finally, we...
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