|
|
Extraction of information from multidimensional data and its visualization
Vansa, Tibor ; Zvára, Karel (referee) ; Ranocha, Pavel (advisor)
The presented thesis aims to describe and compare methods of extraction of information from high dimensional data, with both continuous and discrete variables. It is focused on principal component analysis, factor analysis, multidimensional scaling and correspondence analysis. The thesis includes generalization of multidimensional scaling and correspondence analysis to case with more random variables. Mutual relations of presented methods are studied. Presented methods are applied on real data and their implementation in statistical softwares R and SPSS is desribed.
|
|
|
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.
|
|
|
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.
|
|
|
Multicollinearity
Dřizgová, Lucie ; Hlávka, Zdeněk (referee) ; Zvára, Karel (advisor)
In our work, we explored multicollinearity problem from a complex point of view - from diagnostic methods to the solving of the problems which are caused by the multicollinearity. We compared the Least Squares method with some alternative methods - Principal Component Regression, Partial Least Squares Regression and Ridge Regression on the theoretical basis. In the last section, we demonstrated all methods on practical example computed in the program R.
|
|
|
Rounding procedure
Chudoba, Martin ; Zvára, Karel (referee) ; Lachout, Petr (advisor)
In the presented work, we are introduced to the problem of rounding. In the process of numerous human activities, we nd a need, due to various reasons, to divide nite number of objects according to given ratios which cannot be ful lled exactly. Few basic methods have been developed throughout the history, but they were usually designed ad hoc, without appropriate mathematical background. "Fair" method should enjoy several well de ned properties or not allow some undesirable phenomenona. To avoid such paradoxes, restriction to so-called divisor methods is necessary. Within this group, methods should be inspected under additional criteria - mainly the propensity to prefer larger or smaller subjects, bias. Webster's method (Sainte-Lag ue) stands out as the unique unbiased divisor method, also featuring other important qualities. Real data comparison of chosen methods' most important properties is the nal part of this thesis.
|
|
|
Statistical methods for evaluation of predictive validity
Rubešová, Jana ; Zvára, Karel (advisor) ; Stehlík, Eduard (referee) ; Půlpán, Zdeněk (referee)
Práce pojednává o statistických metodách a modelech, které lze použítpro hledání a analýzu faktorůovlivňujících budoucí úspěšnostve studiu vysoké školy. Jedná se o problémy řešenév celosvětovém měřítku. Pro zkoumání závislosti konečnéhoprůměru známek na dříve známých ve. ličinách jsou využity modely mnohonásobné lineární regrese. Důrazje kladen téžna méně běžnépostupy pro porovnání síly vlivu jednotlivých regresorů. Model logistické regrese' kdy odhadujeme pravděpodobnost úspěchu ve studiu (dané konkrétním kritériem), je doplněn analýzou RoC křivek. Analýzy provedené na datovém souboru 1340 studentů Univerzity Karlovy v Praze, Přírodovědecké fakulty, kteří se zapsali ke studiu bakalářských studij- ních programů v roce 2003104 a2004f05, jsou porovnány s dalšímistudiemi zabývajícímise predikčnívaliditou. Abstract The thesis deals with statistical methods and models suitable to analyze factors that may have influence on future success in graduation. These problems are solved all over the world. Multiple regression models are used for detection dependence final college grade points average on other known variables like admission exam scores and high school grades. The thesis emphasizes less usual methods for comparing effect power of regressors. Logistic regression models where we estimate pro-...
|
|
| |
|
|
Effect of indicators on adjusted score in English language test MANA 2005
Protivínský, Tomáš ; Zvára, Karel (referee) ; Omelka, Marek (advisor)
N5zev prace: VHv indikatoru na dosa^ene skore v testu z anglickeho jazyka MANA2005 Autor: Tomas" Protivinsky Katedra: Katedra pravdepodobnosti a matematicke statistiky Vedouci bakalarske prace: Ing. Marek Omelka E-mail vedouciho: omelka@karlin.mff.cuni.cz Abstrakt: Prace analyzuje data ziskana testy Maturita naneffsto 2005. Zabyva se vlivem jednotlivych faktoru na dosazene skore z anglickeho jazyka, hodnoti je z hlcdiska jejich vyznamnosti a snazi se odhalit vztahy mezi nimi. Nejdfive uvazuji jednoduche modely s jednim vysve-tlujicim faktorem. Zde jsem se zamčfil pf edevgim na typ Skoly (gymnazium, SOS, SOU) a jeji polohu (die pfislugnosti ke kraji) a pohlavi zaka. V praci take kratce diskutuji mozn6 pficlny pozorovanych rozdilu. Tyto dilcl vysledky pak na zdv^r porovnavam s celkovou analyzou, ktera do modelu zahr- nuje vSechny sledovane faktory. Zahrnul jsem i strucny popis zamgfeni a organizace testu Maturitananecisto. Klicova slova: Linearni regrese, analyza rozptylu Title: Effect of indicators on adjusted score in Englishlanguage test MANA 2005 Author: TomaS Protivinsky Department: Department of Probability and Mathematical Statistics Supervisor: Ing. Marek Omelka Supervisor's e-mail address: omelka@karlin.inff.cuni.cz Abstract:The thesis analyzes a data acquired in the test Maturita naneclsto 2005. It...
|
|
| |
|
|
Linear model with near replicates
Smetanová, Pavla ; Anděl, Jiří (referee) ; Zvára, Karel (advisor)
V regresní analýze je nespornou výhodou, máme-li k dispozici opakovaná pozorování. Tato práce se zabývá situací, kdy opakovaná pozorování nemáme, ale máme k dispozici pozorování, která si jsou blízká. V takovém případě rozdělíme pozorování do skupin blízkých pozorování a na jejich základě Jormulujeme testy pro ověření adekvátnosti popisu dat modelem. Takovýchto testů je hned několik. Každá testová statistika je založena na podílu součtu čtverců nedostatku shody a součtu čtverců " čisté" chyby a vynásob na podílem příslušných stupňů volnosti a má F rozdělení. Nedostatek shody modelu s daty můžeme rozlišit na nedostatek shody uvnitř skupin a mezi skupinami. Program R nám poslouží k praktické ukázce vše ch testů.
|
guest ::
