Browsing by Subject "consistency"

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Bootstrap blokowy dla funkcji autokowariancji szeregów czasowych o strukturze okresowej
(Data obrony: 2014-09-15) Chabior, Tomasz
Wydział Matematyki Stosowanej
Access status: Restricted ,
Bootstrap dla modelu AR(p)-ARCH(q)
(Data obrony: 2015-07-02) Kosmala, Miłosz
Wydział Matematyki Stosowanej
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Bootstrap w prawie okresowych szeregach czasowych
(Data obrony: 2014-09-22) Uzar, Jakub
Wydział Matematyki Stosowanej
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Cyclostationary models and their applications
(Data obrony: 2015-10-30) Knapik, Joanna
Wydział Matematyki Stosowanej
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Metoda bloków zwężających dla szeregów czasowych
(Data obrony: 2015-07-02) Krupa, Arkadiusz
Wydział Matematyki Stosowanej
Access status: Open Access ,
Metody resamplingu dla procesów punktowych
(Data obrony: 2009) Dudek, Anna
Wydział Matematyki Stosowanej
Theory of point processes is used for modelling the phenomena of random location of points in some space. Examples of such points are epicenters of earthquakes, location of foxholes in a wood or times of arrivals in a call center. Statistical analysis of such processes is based on some notion of repeatability, usually provided by the assumptions of stationarity. Unfortunately, in many situations the stationarity assumption is not valid. In this work an example of a nonstationary counting process that can be described by the periodic multiplicative intensity model is considered. Such process was chosen because in many applications we encounter phenomena that are periodic in time. These are: the intensity of births during a year, daily car traffic, the number of sales during a year or the network traffic intensity. Known resampling techniques cannot be directly applied in these situations. The reason is that they work well only for the stationary case where sampling blocks and changing their relative positions in the whole sample produces consistent results. The thesis solves this problem via introducing a novel bootstrap technique that respects the temporal order and does not destroy the dependence structure of the data. New bootstrap method is applied to three different estimators of the periodic hazard function. It is shown that the consistent results are obtained in one and multidimensional case. Finally, the bootstrap pointwise and simultaneous confidence intervals are constructed. Their actual coverage probabilities are close to nominal ones independently of the the shape of the considered function. Additionally, the asymptotic simultaneous confidence intervals are hard to calculate and using bootstrap methods seems to be a good alternative. The integrated hazard function case is also considered. The advantages of the proposed 4 Abstract bootstrap simultaneous confidence bands over the asymptotic ones are discussed. Our results are illustrated by an extensive simulation study and analysis of applications based on real data.
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Metody różnicowe typu Cranka-Nicolsona
(Data obrony: 2015-03-03) Lewińska, Paulina
Wydział Matematyki Stosowanej
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Optymalny wybór długości bloku dla metod bootstrapu blokowego
(Data obrony: 2013-07-11) Potorski, Paweł
Wydział Matematyki Stosowanej
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Otwarto-zamknięte ogólne metody liniowe dla równań różniczkowych zwyczajnych
(Data obrony: 2018-07-18) Pierzchała, Paulina
Wydział Matematyki Stosowanej
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Porównanie różnych modeli teorii aksjomatycznych
(Data obrony: 2011-07-13) Baryła, Justyna
Wydział Matematyki Stosowanej
Access status: Open Access ,
Smoothed estimator of the periodic hazard function
(2009) Dudek, Anna
A smoothed estimator of the periodic hazard function is considered and its asymptotic probability distribution and bootstrap simultaneous confidence intervals are derived. Moreover, consistency of the bootstrap method is proved and some applications of the developed theory are presented. The bootstrap method is based on the phase-consistent resampling scheme developed in Dudek and Leśkow [A. Dudek, J. Leśkow, Bootstrap algorithm in periodic multiplicative intensity model, to appear].
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Subsampling dla funkcji autokowariancji szeregów czasowych o strukturze okresowej
(Data obrony: 2014-09-10) Chołody, Marcin
Wydział Matematyki Stosowanej
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Teoria L-estymatorów i M-estymatorów
(Data obrony: 2015-09-30) Wardzała, Paulina
Wydział Matematyki Stosowanej