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Estimation of the pair correlation function of a point process
Vondráček, Jakub ; Dvořák, Jiří (advisor) ; Beneš, Viktor (referee)
This thesis deals with kernel estimation of the pair correlation function of a stationary and isotropic point process. Firstly, the basics of the theory of point processes are built up. Then, the derivation of formulas for expectation and variance of a kernel estimator is provided. Also, an extension of a simple Poisson approximation of variance to the case of an estimator with more complicated edge correction compared to what is usually used in the literature is given. These formulas depend on a parameter called bandwidth. The recommendations for selecting the bandwidth that can be found in the literature are summarised and simulation experiments are performed to assess the correctness of the derived formulas. These experiments also prove that a variance approximation obtained by ignoring so called "higher order correlations" is unjustified. Lastly, bandwidth selection and the advantages and disadvantages of several approaches for bandwidth selection are discussed. 1
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Modern Methods for Image Quality Assessment
Nováček, Petr
This paper deals with the comparison of Image Quality Assessment (IQA) algorithms. The test gallery of colour calibre images were captured for comparison of IQA algorithms. Test gallery was captured by two cameras with a different type of sensors – CMOS with Bayer mask and a Foveon sensor.
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Optimality of sample variance
Gleta, Filip ; Kulich, Michal (advisor) ; Anděl, Jiří (referee)
It is widely known that the most common estimators of the variance and the standard deviation based on i.i.d. data are not optimal with respect to the mean squared error. The aim of this thesis is to study and summarize the various approaches to seeking an improved estimator, which stem mainly from the innovative ideas presented by Stein (1964). Taken into consideration is the point estimator of the variance and the standard deviation. Each of the improved estimators include, in addition to their construction, a discussion regarding admissibility with respect to the MSE. Subsequently, using simple simulations for various distributions, it is examined whether obtained improvements lead to better results in practice. Powered by TCPDF (www.tcpdf.org)
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Variability estimation of development triangles in nonlife insurance
Havlíková, Tereza ; Branda, Martin (advisor) ; Mazurová, Lucie (referee)
The aim of this thesis is to describe calculation methods for variability esti- mation of claims reserve in non-life insurance. The thesis focuses on three main categories of models: Mack's stochastic Chain-Ladder, generalized linear models and bootstrap. Both the theoretical and also the empirical parts are included. Empirical part is devoted to application of all the models described above on both real and simulated data. 1
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Credibility approach to claims reserves calculation
Dzugas, Erik ; Mazurová, Lucie (advisor) ; Pešta, Michal (referee)
In this work we summarize the various techniques of claims reserves evaluating which consist in estimate of the future uncertain and hardly antici- pated loss development. It appears that the methods which are based on some credibility formula bring in the mean squared error sense the most accurate results. We consider this in the text derived conclusion very relevant and con- tributing, therefore we illustrate and present it on the numerical example. The calculations are introduced in the attached charts that build the important sup- plement of the text. The topic of this work follows up the content of Nonlife Insurance and Risk Theory lectures, therefore this text can be useful also for the students of the Faculty of Mathematics and Physics to extend their knowledge. 1
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Statistical hypothesis testing using sports data
Černý, Jakub ; Malá, Ivana (advisor) ; Čabla, Adam (referee)
This bachelor thesis is based on empirical study of betting odds of six world-wide betting offices. Using statistical hypothesis testing it tests similarity among offices predictions of five best football leagues and whether the predictions correspond with final results of these games. It has been demonstrated that betting offices predict matches identically but predictions does not correspond with final results. In the second part of this paper, the betting offices are experimentally treated as bettors and their return on investment is monitored. From the comparison of returns and mean squared error of predictions, betting offices Bet365 and BetVictor can be considered as those with the best predictions. Analysis of Fortel servis betting diary has shown that using betting advisory service can lead to long-term profits. It is a proof that betting offices can be beaten over a long time which was also one of the objectives of this paper.
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