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National Repository of Grey Literature 2 records found  Search took 0.01 seconds. 
Homoscedasticity Tests in a Linear Model
 Vávra, Jan ; Komárek, Arnošt (advisor) ; Hlávka, Zdeněk (referee)
This thesis deals with testing the assumption of homoscedasticity in linear model, that is the assumption of constant variance of this model. There is plenty of such tests, but not all of them can be applied to specific model and not all of them reach satisfactory results under various circumstances. Thesis focuses on tests which can be derived on the basis of the asymptotic theory for maximum likelihood estimation, particularly the test theory with nuisance parameters. There are derived two basic tests, the first one in the situation of analysis of variance model and the second one in the situation when we allow the dependence of variance to concomitant quantities. In subsequent numerical studies there are examined characteristics of derived test statistics. Powered by TCPDF (www.tcpdf.org)
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Analysis of variance when the assumption of homoscedasticity is violated
 Zavadilová, Anna ; Omelka, Marek (advisor) ; Komárek, Arnošt (referee)
The method known as analysis of variance of simple sort offers a possibility of how to test equality of mean values of several random selections. At the same time, however, it requires the random selections to originate from normal distribution and to meet the condition of homoscedasticity, i.e. the requirement of identity of variances. The aim of this Thesis is to analyse consequences of violation of the assumptions of normality and homoscedasticity of the input data. The first part of the Thesis presents an overview of the course of the method based on the analysis of variance with standard assumptions. It is followed by the deriving of asymptotic distribution of test statistics, supposing the validity of the null hypothesis of identity of mean values in the case that neither the normality of input data nor the identity of variances is supposed. The findings are then applied to several special cases. The final part of the Thesis deals with a simulation study describing the influence of non-fulfilment of assumptions imposed on the test significance level. Powered by TCPDF (www.tcpdf.org)
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