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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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Statistical inference based on saddlepoint approximations
Sabolová, Radka ; Jurečková, Jana (advisor) ; Hlávka, Zdeněk (referee) ; Picek, Jan (referee)
Title: Statistical inference based on saddlepoint approximations Author: Radka Sabolová Abstract: The saddlepoint techniques for M-estimators have proved to be very accurate and robust even for small sample sizes. Based on these results, saddle- point approximations of density of regression quantile and saddlepoint tests on the value of regression quantile were derived, both in parametric and nonpara- metric setup. Among these, a test on the value of regression quantile based on the asymptotic distribution of averaged regression quantiles was also proposed and all these tests were compared in a numerical study to the classical tests. Finally, special case of Kullback-Leibler divergence in exponential family was studied and saddlepoint approximations of the density of maximum likelihood estimator and sufficient statistic were also derived using this divergence. 1
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Statistical inference based on saddlepoint approximations
Sabolová, Radka
Title: Statistical inference based on saddlepoint approximations Author: Radka Sabolová Abstract: The saddlepoint techniques for M-estimators have proved to be very accurate and robust even for small sample sizes. Based on these results, saddle- point approximations of density of regression quantile and saddlepoint tests on the value of regression quantile were derived, both in parametric and nonpara- metric setup. Among these, a test on the value of regression quantile based on the asymptotic distribution of averaged regression quantiles was also proposed and all these tests were compared in a numerical study to the classical tests. Finally, special case of Kullback-Leibler divergence in exponential family was studied and saddlepoint approximations of the density of maximum likelihood estimator and sufficient statistic were also derived using this divergence. 1
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Statistical inference based on saddlepoint approximations
Sabolová, Radka
Title: Statistical inference based on saddlepoint approximations Author: Radka Sabolová Abstract: The saddlepoint techniques for M-estimators have proved to be very accurate and robust even for small sample sizes. Based on these results, saddle- point approximations of density of regression quantile and saddlepoint tests on the value of regression quantile were derived, both in parametric and nonpara- metric setup. Among these, a test on the value of regression quantile based on the asymptotic distribution of averaged regression quantiles was also proposed and all these tests were compared in a numerical study to the classical tests. Finally, special case of Kullback-Leibler divergence in exponential family was studied and saddlepoint approximations of the density of maximum likelihood estimator and sufficient statistic were also derived using this divergence. 1
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Statistical inference based on saddlepoint approximations
Sabolová, Radka ; Jurečková, Jana (advisor) ; Hlávka, Zdeněk (referee) ; Picek, Jan (referee)
Title: Statistical inference based on saddlepoint approximations Author: Radka Sabolová Abstract: The saddlepoint techniques for M-estimators have proved to be very accurate and robust even for small sample sizes. Based on these results, saddle- point approximations of density of regression quantile and saddlepoint tests on the value of regression quantile were derived, both in parametric and nonpara- metric setup. Among these, a test on the value of regression quantile based on the asymptotic distribution of averaged regression quantiles was also proposed and all these tests were compared in a numerical study to the classical tests. Finally, special case of Kullback-Leibler divergence in exponential family was studied and saddlepoint approximations of the density of maximum likelihood estimator and sufficient statistic were also derived using this divergence. 1
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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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Normality tests
Kotlorz, Lukáš ; Anděl, Jiří (advisor) ; Sabolová, Radka (referee)
The aim of this thesis focused on testing normality is to describe both statistical tests and graphical methods. The first part is devoted to graphical methods used to testing normality (particularly Histogram, Boxplot and Q-Q Plot). The tests used for testing the conformity of random sample distribution with normal distribution, e.g., Shapiro-Wilk, Kolmogorov-Smirnov, Lilliefors, Anderson-Darling, Chi-squared, are described in the second part. The test statistics, the critical region and alternatively the link for tabulated critical values are listed for each test. The simulations, whether the random sample comes from normal distribution, are described in the third part. The samples from di erent distributions were generated by Program R.
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