National Repository of Grey Literature 158 records found  previous11 - 20nextend  jump to record: Search took 0.01 seconds. 
Independence testing for series of Poisson variables
Jurčo, Tomáš ; Hudecová, Šárka (advisor) ; Hlávka, Zdeněk (referee)
This thesis deals with tests of independence for time series of identically distributed Poisson random variables. In the introductory part, important terms and definitions are defined, in particular the autocorrelation function, its estimates and INAR(1) model. Three types of tests of independence are described in the thesis - tests based on estimates of the autocorrelation function, simple runs test and tests based on contingency tables. These tests are compared in a simulation study under the null hypothesis of independence and under the alternative of INAR(1) model. 1
Semiparametric Analysis of Nested Case-Control Design
Strachoňová, Karla ; Kulich, Michal (advisor) ; Hlávka, Zdeněk (referee)
Studying rare diseases often deals with small percentage of cases requiring a large amount of subjects in the medical study. The common analysis by the Cox proportional hazards model may be very time-consuming and financially inefficient. Nested case- control design presents a sampling method offering fewer data needed for the analysis while keeping the estimator of the Cox model consistent and asymptotic normal. In this thesis, we introduce nested case-control design, we describe in detail the method for sampling controls for cases, we present the partial likelihood and the maximum partial likelihood estimator of the regression parameter and we prove the consistency and the asymptotic normality of the estimator. Then, we introduce the counter-matching design as an extension of the nested case-control design and the pseudolikelihood approach under nested case-control design. In the last chapter, we perform a simulation study comparing the four designs. The contribution of this thesis is the detailed introduction to nested case- control design and its alternatives, more detailed proofs of the asymptotic properties of the maximum partial likelihood of the regression parameter of nested case-control design and the comparison of the four approaches through the simulation study. 1
Model averaging
Trusina, Filip ; Hlávka, Zdeněk (advisor) ; Antoch, Jaromír (referee)
The thesis aims to describe the method of model averaging and the construction of confidence intervals for dose estimation within the method MCP-Mod that is used for modeling the dose-response relationship. We define the doses EDp and MED, which are estimated in practice. We describe the MCP-Mod method, including suitable mod- els and contrast tests. We present information criteria, the ability to determine model weights based on information criteria and discuss their behaviour for different models and a growing number of observations. We also introduce three possible ways of con- structing confidence intervals for estimates obtained using the model averaging method. We apply these constructs to the example of dose-response modeling in a simulation study. Lastly, we introduce two new models with two change-points for modeling the dose-response relationship. 1
Gini coefficient maximization in binary logistic regression
Říha, Samuel ; Hanzák, Tomáš (advisor) ; Hlávka, Zdeněk (referee)
This Bachelor thesis describes a binary logistic regression model. By means of the term loss function a parameter estimation for the model is derived. A "rich" set of "proper" loss functions - beta family of Fisher-consistent loss functions - is defined. In the second part of the thesis, four basic goodness-of-fit criteria - Gini coefficient, C-statistics, Kolmogorov-Smirnov statistics and coefficient of determination R2 are defined. Further on, a possibility of parameter estimation by maximizing the Gini coefficient is analysed. Several algorithms are designed for this purpose. They are compared with so far existing methods in one simulated data set and three real ones. 1
Multivariate goodness-of-fit tests
Kuc, Petr ; Hlávka, Zdeněk (advisor) ; Antoch, Jaromír (referee)
In this thesis we introduce, implement and compare several multivariate goodness-of-fit tests. First of all, we will focus on universal mul- tivariate tests that do not place any assumptions on parametric families of null distributions. Thereafter, we will be concerned with testing of multi- variate normality and, by using Monte Carlo simulations, we will compare power of five different tests of bivariate normality against several alternati- ves. Then we describe multivariate skew-normal distribution and propose a new test of multivariate skew-normality based on empirical moment genera- ting functions. In the final analysis, we compare its power with other tests of multivariate skew-normality. 1
Gradual change model
Míchal, Petr ; Hlávka, Zdeněk (advisor) ; Pešta, Michal (referee)
The thesis aims at change-point estimation in gradual change models. Methods avail- able in literature are reviewed and modified for point-of-stabilisation (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 change-point, 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 change-point 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
Modelling dependence between hydrological and meteorological variables measured on several stations
Turčičová, Marie ; Jarušková, Daniela (advisor) ; Hlávka, Zdeněk (referee)
Title: Modelling dependence between hydrological and meteorological variables measured on several stations Author: Bc. Marie Turčičová Department: Department of Probability and Mathematical Statistics Supervisor: Prof. RNDr. Daniela Jarušková CSc., Czech Technical University in Prague, Faculty of Civil Engineering, Department of Mathematics Abstract: The aim of the thesis is to explore the dependence of daily discharge averages of the Opava river on high daily precipitation values in its basin. Three methods are presented that can be used for analyzing the dependence between high values of random variables. Their application on the studied data is also given. First it is the tail-dependence coefficient that measures the dependence between high values of two continuous random variables. The model for the high quantiles of the discharge at a given precipitation value was first determined non-parametrically by quantile regression and then parametrically through the peaks-over-threshold (POT) method. Keywords: extremal dependence, tail-dependence coefficient, quantile regression, peaks over threshold method
The Kelly Criterion
Kálosi, Szilárd ; Omelka, Marek (advisor) ; Hlávka, Zdeněk (referee)
The present work is devoted to the Kelly criterion, which is a simple method for choosing the amount of the bet for gambles with a positive expected value. In the first part of the work we introduce the mathematical explanation of the criterion, examine the capital after $n$ trials as a function of the bet, the long-run rate of return and asymptotical properties of the capital growth. In the second part we attempt to generalize the Kelly criterion from the first part for some other situations. Examples for a simple game and generalized situations illustrating the properties of the Kelly criterion and results from previous parts compose the last part of the work.
Errors in Variables
Mordinová, Katarína ; Hlávka, Zdeněk (advisor) ; Komárek, Arnošt (referee)
1 Title: Errors in variables Author: Katarína Mordinová Department: Department of Probability and Mathematical Statistics Supervisor: Mgr. Zdeněk Hlávka, Ph.D. Supervisor's e-mail address: Zdenek.Hlavka@mff.cuni.cz Abstract: The topic of the diploma thesis is Errors in variables. In the opening chapter, we define basic terms used in the thesis and we introduce the regression analysis and basic relations related to this term. In the second chapter, we attend to linear regression model and its characteristics. In the third chapter, we attend to the errors in variables models. In the last chapter of this thesis we present a possible application in medicine. Keywords: regresion analysis, errors in variables, linear regression model

National Repository of Grey Literature : 158 records found   previous11 - 20nextend  jump to record:
Interested in being notified about new results for this query?
Subscribe to the RSS feed.