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Paired tests with missing observations
Sionová, Kristýna ; Kulich, Michal (referee) ; Zvára, Karel (advisor)
The aim of this work is to find procedures for testing the equality of means of a bivariate normal distribution when observations are missing on one or both variables. One of the possible solutions is to discard the incomplete data and to use the paired t test. In this thesis we describe tests that enable using all available data. For the case of missing observations on one variable, the solutions of Banerjee, Welch and Mehta and Gurland are presented. For the case of missing observations on both variables, the solutions of Banerjee, Welch, Bhoj and the solution based on the maximal likelihood estimate are presented. We compare the solutions found to each other and to the paired t test on simulated data. The software R 2.5.1 is used for this purpose.
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Tests of normality of time series
Stibůrek, David ; Kulich, Michal (referee) ; Anděl, Jiří (advisor)
This work considers testing normality of time series in AR and ARMA processes. Firstly we investigate properties of common normality tests, which assume independency. The main goal is to examine levels and powers of tests in dependence on distances of the roots of the characteristic polynom from unit circle. After this we study the tests, which don't assume independency. In the case of AR processes, we get good results by testing normality of residuals. More complex tests can also give good results, but these tests need many observations and are difficult from the numerical point of view.
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Analysis of change from baseline to post-intervention value
Pacáková, Andrea ; Hlávka, Zdeněk (referee) ; Kulich, Michal (advisor)
The aim of the present work is to compare three di erent estimators of a treatment e ect in clinical randomized studies. The purpose of these studies is to compare the change of a distribution of certain variable between two attendances. Mentioned estimators were developed from the assumption of validity of some model. In this work we gather properties of the estimators when each of all given models is valid. We deal with the consistency of the estimators and with their asymptotic distributions and then we compare the estimators on the basis of their asymptotic variances. In the most of cases is possible to make the comparison in general. In the case when it is not possible, we show a few particular examples. Eventually, we accomplish the simulation study, which certi es theoretical conclusions and extends pieces of knowledge in the cases when it was not possible to make theoretical computation in general.
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Properties of two-phase testing procedures
Krausová, Eliška ; Omelka, Marek (referee) ; Kulich, Michal (advisor)
In the present work we study properties of two-phase testing procedures which formally verify assumptions by performing some test ( first phase) and subsequently calculate a test statistic selected according to the results of the previous test (second phase). In the beginning we describe two-phase testing procedures and mention some literature, in which they are recommended. We try to derive formula for the combined level and power of the whole two-phase testing procedure. After that we illustrate their properties through simulation studies.
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Effect of measurement error on the shape of the regression function in nonlinear models
Drábková, Alena ; Zvára, Karel (referee) ; Kulich, Michal (advisor)
In this thesis we study the effect of regressors measured with an error on an estimated coefficients in a generalized linear model. We infer the true shape of the mean and of the variance function in the given model. We show that assumptions of a generalized linear model are not fulfilled universally if we use variables measured with an error. Despite this, the error-in-variable model can still be useful for testing dependence of original correct regressor. Further on in the thesis, the asymptotic values of coefficients are approximated, assuming g(E(Yi|Wi)) is a quadratic function. Examples for all results are provided through simulations.
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Parameter estimation in case-cohort studies
Klášterecký, Petr ; Kulich, Michal (advisor) ; Volf, Petr (referee) ; Komárek, Arnošt (referee)
The concern of this thesis is parameter estimation in regression models in survival analysis, particularly in case-cohort studies. In case-cohort studies, observations are sampled to form a subcohort which is followed and analysed. As a result, the cost of performing such studies is reduced but standard procedures for parameter estimation need to be modified. This is usually done by incorporating weights into the estimating equations so that individual sampling probabilities are accounted for. In this thesis we show that this method can lead to biased estimators when the subcohort sampling probability is low and suggest an alternative estimator based on logistic regression.
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Regression models for intensities of failures in the reliability analysis
Novák, Petr ; Kulich, Michal (referee) ; Volf, Petr (advisor)
In the present work we study regression models in reliability analysis. We compare the Cox proportional hazards model, Aalen additive model, accelerated failure time model and their combinations. For each model we present procedures for estimating parametric and non-parametric risk function parts and goodness-of-fit tests based on classic regression routines and counting process theory. We demonstrate those tests on both real and simulated data and we focus on procedures how to find the model with the best fit.
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