|
|
Introduction to Nonparametric Methods
Prelecová, Natália ; Kulich, Michal (advisor) ; Navrátil, Radim (referee)
Title: Introduction to Nonparametric Methods Author: Natália Prelecová Department: Department of Probability and Mathematical Statistics Supervisor: doc. Mgr. Michal Kulich,Ph.D., Department of Probability and Mathematical Statistics Abstract: The aim of this thesis is to introduce basic nonparametric methods. Nonparametric methods embrace a large class of statistical procedures which do not assume specific data distribution such as normal distribution. They often re- present the only available means of examining specific types of data, for example ranks or counts. Weaker assumptions of these methods make them less powerful than their parametric counterparts. This thesis describes in detail four nonparametric tests- the Ordinary Sign Test, the Wilcoxon Signed-rank Test, the Mann-Whitney Test and finally the Two- sample Wilcoxon Test. The structure of their description will entail the following: the formulation of assumptions, null hypothesis and alternatives, the construction of the test statistic and the definition of rejection regions. The most essential prob- lems, such as the problem of ties, will be also covered. The basic characteristics of the Linear Rank Statistics will be also explained, followed by the Two-sample Wilcoxon test. Keywords: nonparametrical, hypothesis, ranks, consistency, statistic
|
|
| |
|
|
Methods for Analyzing Change From Baseline to Final Assessment
Pekařová, Lucie ; Kulich, Michal (advisor) ; Hušková, Marie (referee)
In this thesis, we analyze treatment effect estimate in randomized clinical studies. Treatment effect estimates are constructed on the basis of three models. The first part of this thesis is about the behaviour of these estimates when the treatment effects vary with patients. We find out that all types of estimates are consistent and we derived their asymptotic distribution. The estimates are compared by their asymptotic variances. The theoretical conclusions are confirmed by a simulation study. The second part describes the case where measurements of baseline and final values contain an error. Two estimates are analyzed. We find out that both estimates are consistent. We derive their asymptotic distribution and compare their variances.
|
|
|
Odhad momentů při intervalovém cenzorování typu I
Ďurčík, Matej ; Komárek, Arnošt (advisor) ; Kulich, Michal (referee)
Title: Moments Estimation under Type I Interval Censoring Author: Matej Ďurčík Department: Faculty of Probability and Mathematical Statistics Supervisor: RNDr. Arnošt Komárek Ph.D. Abstract: In this thesis we apply the uniform deconvolution model to the interval censoring problem. We restrict ourselves only on interval censoring case 1. We show how to apply uniform deconvolution model in estimating the probability distribution characteristics in the interval censoring case 1. Moreover we derive limit distributions of the estimators of mean and variance. Then we compare these estimators to the asymptotically efficient estimators based on the nonparametric maximum likelihood estimation by simulation studies under some certain distributions of the random variables. 1
|
|
|
Hardy-Weinberg equlibrium
Vlčková, Katarína ; Zvára, Karel (advisor) ; Kulich, Michal (referee)
In this paper, we describe various tests used to determine deviations from the Hardy-Weinberg equilibrium. The tests described are: the exact test, the χ2 test with and without continuity correction, the conditional χ2 test with and without continuity correction and the likelihood ratio test. These tests explore the question whether a random sample has trinomic distribution with probabilities pAA = θ2 , pAa = 2θ(1 − θ), paa = (1 − θ)2 . In this work, we simulate data of sample size 100 and we estimate the probability of type I error and the power of the tests. In this case, we get the best results with conditional χ2 test. The estimate of the power of the likelihood ratio test and the χ2 test is one of the highest of all. On the other hand, these two test are anticonservative in some cases . 1
|
|
|
Classification based on longitudinal observations
Bandas, Lukáš ; Komárek, Arnošt (advisor) ; Kulich, Michal (referee)
The concern of this thesis is to discuss classification of different objects based on longitudinal observations. In the first instance the reader is introduced to a linear mixed-effects model which is useful for longitudinal data modeling. Description of discriminant analysis methods follows. These methods ares usually used for classification based on longitudinal observations. Individual methods are introduced in the theoretic aspect. Random effects approach is generalized to continuous time. Subsequently the methods and features of the linear mixed-effects model are applied to real data. Finally features of the methods are studied with help of simulations.
|
|
|
Simpson's paradox
Balhar, Jan ; Komárek, Arnošt (advisor) ; Kulich, Michal (referee)
Title: Simpson's paradox Author: Jan Balhar Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Arnošt Komárek, Ph.D. Supervisor's e-mail address: arnost.komarek@mff.cuni.cz Abstract: In this work we deal with Simpson's paradox and its more general version, called association reversal. We present definitions of these terms and necessary and sufficient conditions for their occurrence. Due to this, we get to issue of measuring relationship between two characters in 2x2 contigency table, we specifically mention advantages of odds ratio. We also try to answer, what relationship between two characters is, in case of Simpson's paradox, the right one. When looking for answer, we find, that ordinary statistical methods are not sufficient. It is necessary to identify causal relationships between characters. Therefore we get to issue of causality definition. Finally, we present some examples of Simpson's paradox in practice. Keywords: Simpson's paradox, association reversal, confounding, causality.
|
|
|
Introduction to Bayesian Data Analysis
Štádlerová, Kateřina ; Kulich, Michal (advisor) ; Anděl, Jiří (referee)
of the bachelor's thesis Title: Introduction to Bayesian Data Analysis Author: Kateřina Štádlerová Department: Department of Probability and Mathematical Statistics Supervisor: doc. Mgr. Michal Kulich, Ph.D., Department of Probability and Mathematical Statistics Abstract: The paper deals with basic principles of Bayesian methods. These me- thods have very broad range of use in statistical problems concerning estimation and hypothesis testing. However, their use is much wider; these methods are used in anti-spam filters of electronic mail or in the game theory. Definitions, theo- rems, proofs and examples are included in the paper for this purpose to enable easier understanding of particular topics. The paper is helpful mainly because of the fact that as yet there are not many books in Czech language dealing with Bayesian methods. 1
|
|
| |
|
|
Statistická analýza přežití a incidenční funkce
Djordjilović, Vera ; Volf, Petr (advisor) ; Kulich, Michal (referee)
Competing risks occur often in survival analysis. In present work, we study different ap- proaches to modeling competing risks data and use examples to illustrate the most impor- tant results. In the competing risks setting it is often of interest to calculate the cumulative incidence of a specific event. We first study non-parametric estimation and then present three approaches to regression modeling. We use simple numerical example to demonstrate the use of non-parametric methods and perform analysis of real data from Stanford Heart Transplant Program to illustrate and compare the chosen regression models.
|
guest ::
RSS feed.