
Methods for Constrained State Estimation: Comparison and Application to ZeroBound Interest Rate Problem
Musil, Karel ; Hlávka, Zdeněk (referee)
The thesis introduces an overview of techniques for filtering of unobserved variables using a statespace representation of a model and state inequality constraints. It is mainly aimed at a derivation of the linear Kalman filter and imposing state constraints. The state uniform model with noise bounds and the sequential importance sampling, as a method of particle filters using Monte Carlo simulations, are described as alternative methods. These three methods are applied on a simple semistructural model for a monetary policy analysis. The filtration is based on Czech macroeconomic data and reflects an imposed timevarying nonnegative state constraint on the nominal interest rate. Results of the algorithms are compared and discussed. Powered by TCPDF (www.tcpdf.org)

 

Nonlienar volatility modeling in financial time series
Sychova, Maryna ; Zichová, Jitka (advisor) ; Hlávka, Zdeněk (referee)
In this work we want to examine selected models with nonlinear volatility and their properties. At the beginning we define models with nonconstant variance, especially ARCH, GARCH and EGARCH models. Then we study the probability distributions that are mainly used in the EGARCH model. Then we focus on the EGARCH model, describe the conditions for stationarity and invertibility of the model, define diagnostic tests and QMLE estimates of parameters. In the last chapter we perform simulation studies of the selected models and their application to real data. 1


Distribution of interpoint distances
Horská, Šárka ; Hlávka, Zdeněk (advisor) ; Komárek, Arnošt (referee)
This thesis investigates basic properties of the interpoint distances be tween random vectors drawn from multinomial distribution. We also describe a possible application to testing sparse observations, i.e., a setup with small number of observations and large number of categories, where the classical χ2 test cannot be recommended. As an alternative, utilizing the multinomial interpoint distances, we will present the test statistic proposed by Biswas and Ghosh (2014). 1


Doseresponse curves
Hezoučký, Martin ; Hlávka, Zdeněk (advisor) ; Maciak, Matúš (referee)
Title: Doseresponse curves Author: Martin Hezoučký Department: Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Zdeněk Hlávka, Ph.D., Department of Probability and Mathematical Statistics Abstract: In this thesis, we deal with the process of research and development of new medical substances with a focus on statistical methods used to determine appropriate doses. For this purpose, we examine the doseresponse relationship. First, we describe a typical procedure for the development of a new drug. Second, we focus in detail on the MCPMod method. Third, we propose a new method based on the theory of gradual change models. This approach tests whether the administration of the drug has a significant effect. If so, the dose with desired effect is estimated using an appropriate model. Specifically, we provide an esti mate using linear, quadratic and Emax gradual change models. We also describe a construction of a confidence interval for the point of change and also for the dose with the desired effect. The advantage of the proposed method over the MCPMod is the determination of the confidence intervals. Finally, we apply the above mentioned methods to data from the U.S. Tox21 research program and compare the results based on several tested substances and clearly demonstrate the...


Gradual change model
Míchal, Petr ; Hlávka, Zdeněk (advisor) ; Pešta, Michal (referee)
The thesis aims at changepoint estimation in gradual change models. Methods avail able in literature are reviewed and modified for pointofstabilisation (PoSt) context, present e.g. in drug continuous manufacturing. We describe in detail the estimation in the linear PoSt model and we extend the methods to quadratic and Emax model. We describe construction of confidence intervals for the changepoint, discuss their interpre tation and show how they can be used in practice. We also address the situation when the assumption of homoscedasticity is not fulfilled. Next, we run simulations to calculate the coverage of confidence intervals for the changepoint in discussed models using asymp totic results and bootstrap with different parameter combinations. We also inspect the simulated distribution of derived estimators with finite sample. In the last chapter, we discuss the situation when the model for the data is incorrectly specified and we calculate the coverage of confidence intervals using simulations. 1


Bivariate negative binomial distributions
Šír, David ; Hudecová, Šárka (advisor) ; Hlávka, Zdeněk (referee)
The thesis summarizes basic properties of the negative binomial distribution, including estimations of unknown parameters which are derived with the help of the method of moments and the maximum likelihood method. The main part of the thesis describes the bivariate negative binomial distribution. Basic properties of the studied distribution are derived. For instance marginal distribution, distribution of the sum of elements and conditional distribution are negative binomial. The unknown parameters are estimated using the methods of moments and maximum likelihood method. The consistency and asymptotic normality of these estimators are proved. The final sample behaviour of the estimators is investigated in a small simulation study. The described bivariate distribution is applied to real traffic accidents data set from the Czech Republic. 1


Comparison of Models for Probabilities in Football Betting
Kožnar, František ; Večeř, Jan (advisor) ; Hlávka, Zdeněk (referee)
The aim of the thesis is to compare different statistical models for football betting odds and determine the best performing once based on the historical performance of sport teams. There are at least two possible approaches for computing the odds, namely Poisson regression and methods based on statistical machine learning. The idea is that the historical performance of teams is a good predictor of the future performance. Thus we can take the past performances, say all matches in the full season of the Bundesliga (306 matches), and use these data for predicting the odds for the following season. The resulting odds should be compared with the actual results using the scoring rules, which will identify the best performing model. 1


Robust estimation of autocorrelation function
Lain, Michal ; Hudecová, Šárka (advisor) ; Hlávka, Zdeněk (referee)
The autocorrelation function is a basic tool for time series analysis. The clas sical estimation is very sensitive to outliers and can lead to misleading results. This thesis deals with robust estimations of the autocorrelation function, which is more resistant to the outliers than the classical estimation. There are presen ted following approaches: leaving out the outliers from the data, replacement the average with the median, data transformation, the estimation of another coeffici ent, robust estimation of the partial autocorrelation function or linear regression. The thesis describes the applicability of the presented methods, their advantages and disadvantages and necessary assumptions. All the approaches are compared in simulation study and applied to real financial data. 1


Comparison of Models for Probabilities in Football Betting
Kožnar, František ; Večeř, Jan (advisor) ; Hlávka, Zdeněk (referee)
The aim of the thesis is to compare different statistical models for football betting odds and determine the best performing once based on the historical performance of sport teams. There are at least three possible approaches for computing the odds, namely logistic regression, Poisson regression and methods based on statistical machine learning. The idea is that the historical performance of teams is a good predictor of the future performance. Thus we can take the past performances, say all matches in the full season of the English Premier League (380 matches), and use these data for predicting the odds for the following season. The resulting odds should be compared with the actual results using the scoring rules, which will identify the best performing model.
