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National Repository of Grey Literature 2 records found  Search took 0.01 seconds. 
Large dimension of regressors in regression problems
 Semjonov, Valerij ; Omelka, Marek (advisor) ; Mizera, Ivan (referee)
This thesis deals with asymptotic properties of least squares estimators of regression coefficients of linear models with a large dimension of regressors. Particularly, consistency and asymptotic normality are investigated. Several types of consistency are defined and their mutual relation is discussed. Theorems on the asymptotic normality are formulated separately for random and fixed designs. The average proportion of the cases when the true regression coefficients are not covered by the asymptotic confidence intervals is calculated for some chosen linear models by means of simulations. Specifically, for One- way ANOVA these average proportions are compared with the theoretical probabilities given by the derived asymptotic formulae. 1
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Index of dispersion for discrete distributions
 Semjonov, Valerij ; Hudecová, Šárka (advisor) ; Zichová, Jitka (referee)
This thesis deals with the index of dispersion for discrete distributions. In the first chapter, we define the sample index of dispersion and describe it's basic properties , specifically for the Poisson distribution. An asymptotic distribution of the sample index of dispersion will be derived for the Poisson and some other distributions. In the second chapter, we describe the index of dispersion test and determine it's approximate power against some specific alternatives. The third chapter is dedicated to a simulation study in which statistical properties of the test are investigated. Empirical estimation of the power of the test will be compared with the analytical results obtained in the second chapter.
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