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Small sample asymptotics
Tomasy, Tomáš ; Sabolová, Radka (advisor) ; Omelka, Marek (referee)
In this thesis we study the small sample asymptotics. We introduce the saddlepoint approximation which is important to approximate the density of estimator there. To derive this method we need some basic knowledge from probability and statistics, for example the central limit theorem and the M- estimators. They are presented in the first chapter. In practical part of this work we apply the theoretical background on the given M-estimators and selected distribution. We also apply the central limit theorem on our estimators and compare it with small sample asymptotics. At the end we show and summarize the calculated results.
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Edgeworth expansion
Dzurilla, Matúš ; Omelka, Marek (advisor) ; Nagy, Stanislav (referee)
This thesis is focused around Edgeworth's expansion for approximation of distribution for parameter estimation. Aim of the thesis is to introduce term Edgeworth's expansion, its assumptions and terminology associated with it. Afterwards demonstrate process of deducting first term of Edgeworth's expansion. In the end demonstrate this deduction on examples and compare it with different approximations (mainly central limit theorem), and show strong and weak points of Edgeworth's expansion.
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Edgeworth expansion
Dzurilla, Matúš ; Omelka, Marek (advisor) ; Nagy, Stanislav (referee)
This thesis is focused around Edgeworths expansion for aproximation of distribution for parameter estimation. Aim of the thesis is to introduce term Edgeworths expansion, its assumptions and terminology associeted with it. Afterwords demonstrate process of deducting first term of Edgeworths expansion. In the end demonstrate this deduction on examples and compare it with different approximations (mainly central limit theorem), and show strong and weak points of Edgeworths expansion.
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Small sample asymptotics
Tomasy, Tomáš ; Sabolová, Radka (advisor) ; Omelka, Marek (referee)
In this thesis we study the small sample asymptotics. We introduce the saddlepoint approximation which is important to approximate the density of estimator there. To derive this method we need some basic knowledge from probability and statistics, for example the central limit theorem and the M- estimators. They are presented in the first chapter. In practical part of this work we apply the theoretical background on the given M-estimators and selected distribution. We also apply the central limit theorem on our estimators and compare it with small sample asymptotics. At the end we show and summarize the calculated results.
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