National Repository of Grey Literature 92 records found  beginprevious21 - 30nextend  jump to record: Search took 0.00 seconds. 
Ecological regression
Poul, Pavel ; Zvára, Karel (advisor) ; Prášková, Zuzana (referee)
Tato práce se zabývá problémem při analýze dat, který vzniká agre- gací veličin do jednotlivých soubor·, pro které známe pouze pr·měry p·vodních veličin a počty jednotek, ze kterých tento soubor vznikl. Jedná se o problém nedo- statečného množství informací, který zp·sobuje nepřesné stanovení vztah· mezi p·vodními veličinami. Tato práce si klade za cíl detailně seznámit čtenáře s dopa- dy agregace dat, představit jednotlivé možnosti přístupu k problému a představit takové modely a předpoklady, které povedou ke správnému stanovení vztah· me- zi p·vodními veličinami. Práce je zakončena praktickým použitím jednotlivých přístup· na reálných datech. Výpočty jsou prováděny v software R. 1
Outliers
Kudrnáč, Vojtěch ; Zvára, Karel (advisor) ; Anděl, Jiří (referee)
This paper concerns itself with the methods of identifying outliers in an otherwise normally distributed data set. Several significant tests and criteria designed for this purpose are described here, Peirce's criterion, Chauvenet's criterion, Grubbs' test, Dixon's test and Cochran's test. Deriving of the tests and criteria is indicated and finally the results of the use of the test and criteria on simulated data with normal distribution and inserted outlier are looked into. Codes in programming language R with the implementation of these test and criteria using existing functions are included. Powered by TCPDF (www.tcpdf.org)
Seeming regression of economic indices
Komzáková, Magdalena ; Lachout, Petr (advisor) ; Zvára, Karel (referee)
In the time series analysis it often appears that two or more time series influence each other. When the generating stochastic processes of these series do not have stationary structure but they are stochastically non-stationary, i.e. the characteristic polynomial has a unit root, it happens that the regression modelling the dependence of some absolutely independent series gives statistically significant parameter estimations and statistics used to judge the model fitting do not indicate anything about its impropriety. This phenomenon is called seeming regression (spurious regression) and is solved with the theory of cointegration. We can say that when the series are cointegrated, their model shows their real dependence, not only the seeming one. Due to this fact, cointegration tests are also used for testing for the presence of seeming regression. These tests are based on unit root tests in generating process (or on stationarity tests), because time series can be cointegrated only if their linear combination is a stationary series.
Examination of k regression lines
Drozen, Alan ; Zvára, Karel (advisor) ; Omelka, Marek (referee)
In the present work we study the problem of k regression lines in the general linear model. First we describe the general linear model with a multivariate normal distribution of errors and we show some of its basic characteristics. Then we introduce a model with k regression lines. Further, we describe a test for testing the hypothesis of two regression lines being parallel and another one for testing all or some of the k regression lines being parallel or identical. Then we derive the test of the submodel of the general linear model and analyze issues such as the power of this test, the submodel of another submodel, the orthogonality and reparametrization. We show geometric interpretations of the general linear model and of the submodel test as well. In the subsequent part, we focus on nonparametric tests. We present four permutation tests for testing the submodel in the general linear model. Finally we perform numerical simulation to find out whether the tests match the required size and to determine their power.
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
Modeling progression of HIV disease
Žohová, Ivana ; Kulich, Michal (advisor) ; Zvára, Karel (referee)
In the present work we study modeling of HIV disease progression via multistate Markov model. The difficulty in this approach is how to define HIV disease states. These are usually defined in terms of CD4+ T lymphocyte counts, but this marker is a subject to biological fluctuation and, in real life, measurement errors as well. Estimating the model on such a data will lead to intensity estimates depending on frequency of observations. That is why we usually smooth the data before fitting the Markov model. In this work we studied two different approaches - linear mixed-effects model and local polynomial kernel estimator. All modeling is performed on real data and also an illustrative simulation example is included. Another issue considered in this work is determination of sero-conversion time. The sero-conversion distribution is derived based on time of last negative observation, first positive observation and last performed measurement.
Expectation-Maximization Algorithm
Vichr, Jaroslav ; Pešta, Michal (advisor) ; Zvára, Karel (referee)
EM (Expectation-Maximization) algorithm is an iterative method for finding maximum likelihood estimates in cases, when either complete data include missing values or assuming the existence of additional unobserved data points can lead to more simple formulation of the model. Each of its iterations consists of two parts. During the E step (expectation) we calculate the expected value of the log-likelihood function of the complete data, with respect to the observed data and the current estimate of the parameter. The M step (maximization) then finds new estimate, which will maximize the function obtained in the previous step and which will be used in the next iteration in step E. EM algorithm has important use in e.g. price and manage risk of the portfolio.
Confidence intervals for differences and ratios of proportions
Krnáč, Ľuboš ; Kulich, Michal (advisor) ; Zvára, Karel (referee)
The Bachelor thesis deals with the creation of confidence intervals for diffe- rence of parameters of two distributions. In the first part we consider the problem of making such confidence intervals for differences. Then we try to find sufficient conditions for MOVER, which leads to new, non-trivial confidence intervals for difference of parameters of two distributions. These confidence intervals have im- proved and desired properties. There are also examples of usage of MOVER, and possible difficulties. The third section contains graphs of coverage probabili- ties for different input intervals. These graphs are made to show different levels of achieved coverage probabilities for some input intervals, namely Clopper-Pearson, Wald, Wilson and logit. 1

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1 Zvára, K.
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