Browsing by Subject "bootstrap"

Now showing 1 - 12 of 12

Access status: Restricted ,
Cyclostationary models and their applications
(Data obrony: 2015-10-30) Knapik, Joanna
Wydział Matematyki Stosowanej
Access status: Restricted ,
Metody bootstrap dla okresowego modelu multiplikatywnej intensywności
(Data obrony: 2013-07-11) Kozłowski, Piotr
Wydział Matematyki Stosowanej
Access status: Restricted ,
Metody bootstrapowe w problemie Wicksella
(Data obrony: 2015-07-02) Sierpiński, Damian
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.
Access status: Open Access ,
Nonparametric bootstrap confidence bands for unfolding sphere size distributions
(Wydawnictwa AGH, 2021) Wojdyła, Jakub
The stereological inverse problem of unfolding the distribution of spheres radii from measured planar sections radii, known as the Wicksell's corpuscle problem, is considered. The construction of uniform confidence bands based on the smoothed bootstrap in the Wicksell's problem is presented. Theoretical results on the consistency of the proposed bootstrap procedure are given, where the consistency of the bands means that the coverage probability converges to the nominal level. The finite-sample performance of the proposed method is studied via Monte Carlo simulations and compared with the asymptotic (non-bootstrap) solution described in literature.
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O pewnym problemie porównywania charakterystyk testów medycznych
(Data obrony: 2012-09-14) Dworzańska, Karolina
Wydział Matematyki Stosowanej
Access status: Restricted ,
Pasy ufności w modelu regresji nieparametrycznej ze zmiennymi zaburzonymi
(Data obrony: 2017-06-30) Łach, Weronika
Wydział Matematyki Stosowanej
Access status: Restricted ,
Pasy ufności w modelu regresji odwrotnej
(Data obrony: 2017-09-29) Ruszkowicz, Faustyna
Wydział Matematyki Stosowanej
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Punktowe przedziały ufności w modelu odwrotnej regresji
(Data obrony: 2017-11-14) Biel, Michał
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].
Access status: Open Access ,
Tenfold bootstrap procedure for support vector machines
(Wydawnictwa AGH, 2020) Vrigazova, Borislava; Ivanov, Ivan
Cross validation is often used to split input data into training and test sets in support vector machines. The two most commonly used cross validation versions are the tenfold and leave-one-out cross validation. Another commonly used resampling method is the random test/train split. The advantage of these methods is that they avoid overﬁtting in a model and perform model selection. However, they can increase the computational time for ﬁtting support vector machines by increasing the size of the dataset. In this research, we propose an alternative for ﬁtting SVM, which we call the tenfold bootstrap for support vector machines. This resampling procedure can signiﬁcantly reduce execution time despite the large number of observations, while preserving a model’s accuracy. With this ﬁnding, we propose a solution to the problem of slow execution time when ﬁtting support vector machines on big datasets.
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Testowanie losowości procesu występowania wstrząsów w sejsmiczności naturalnej i sejsmiczności indukowanej pracami górniczymi
(Data obrony: 2009-12-21) Letkowska, Magdalena
Wydział Geologii, Geofizyki i Ochrony Środowiska
In M.Sc. thesis the character of the seismic event occurrence process in natural seismicity and seismicity induced by mining works was studied. The investigations were conducted based on data from an active seismogenic area of Greece and on series of mining seismic events from a Polish copper mine. The null hypothesis, assuming that the process of seismic event occurrence was Poissonian was verified. Two parameters were used: the difference between the empirical cumulative distribution of interevent time and the expotential distribution D(t), and the Matsumura’s coefficient of randomness. The bootstrap resampling technique was used for calculating confidence intervals of these parameters.