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The U-statistics
Novák, Petr ; Madurkayová, Barbora (advisor) ; Hušková, Marie (referee)
Nazcv pracc: U-statistiky Autor: IVtr N'ovak Katcdra: Katedra, pravdepodobnosti a matematicke statistiky Vedouci bakalafske pracc: Mgr. Barbora Madurkayova c-tnail vedouciho: niadurkai''i~ikai-liii.inir.cuni.c'/ Abstrakt: V teto praci se budeine zabyvat vehni vyznamnou tfidou sta- tistik, U-statistikami. Tyto json zobecnenim vyberoveho prumeru, vybcro- veho rozptylu i dalsich zuainych statistik. V praci sc nejprve scznamnjeme s prolilciny, ktcrr vcdly k objcvu U-statistik, a jejic:h frsenim. Pf> zavcclcni U-statistik ye soznaniiiiK1 s nektcrynii jcjich vlastno.stini, diky ktcryin json /.name. Dale so bndenic zabyvat jejich ro/]jtyloin a jcho vhodnyin vyjadfe- nini a take kovarianci dvon rnznych U-statistik. Pote odvodiine take odhady pro vyssi momenty U-statistik, ktero pro vrtsiim vypoctu i>ostac\\ji. V dalsi kapitole st! take zniiniiiH1 o II-rozkladn U-statistik. Na '/aver se zamerhne na, spojitost U-statistik y inartiiigaly. Klicova slova: U-statistiky, II-rozklad, Martingal Title: U-statistics Author: Petr .\ov;ik Department: De])a,rtineiit of Probability and Mathematical Statistics Supervisor: Mgr. Barbora Madurkayova Supervisor's c-niail address: madnrka«"karlin.infrcnni.cz Abstract: In this work we consider important class of statistics, U-Statistics. These arc generalisation of .sample mean, sample...
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The U-statistics
Novák, Petr ; Hušková, Marie (referee) ; Madurkayová, Barbora (advisor)
Nazcv pracc: U-statistiky Autor: IVtr N'ovak Katcdra: Katedra, pravdepodobnosti a matematicke statistiky Vedouci bakalafske pracc: Mgr. Barbora Madurkayova c-tnail vedouciho: niadurkai''i~ikai-liii.inir.cuni.c'/ Abstrakt: V teto praci se budeine zabyvat vehni vyznamnou tfidou sta- tistik, U-statistikami. Tyto json zobecnenim vyberoveho prumeru, vybcro- veho rozptylu i dalsich zuainych statistik. V praci sc nejprve scznamnjeme s prolilciny, ktcrr vcdly k objcvu U-statistik, a jejic:h frsenim. Pf> zavcclcni U-statistik ye soznaniiiiK1 s nektcrynii jcjich vlastno.stini, diky ktcryin json /.name. Dale so bndenic zabyvat jejich ro/]jtyloin a jcho vhodnyin vyjadfe- nini a take kovarianci dvon rnznych U-statistik. Pote odvodiine take odhady pro vyssi momenty U-statistik, ktero pro vrtsiim vypoctu i>ostac\\ji. V dalsi kapitole st! take zniiniiiH1 o II-rozkladn U-statistik. Na '/aver se zamerhne na, spojitost U-statistik y inartiiigaly. Klicova slova: U-statistiky, II-rozklad, Martingal Title: U-statistics Author: Petr .\ov;ik Department: De])a,rtineiit of Probability and Mathematical Statistics Supervisor: Mgr. Barbora Madurkayova Supervisor's c-niail address: madnrka«"karlin.infrcnni.cz Abstract: In this work we consider important class of statistics, U-Statistics. These arc generalisation of .sample mean, sample...
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Tests based on U-statistics
Madurkayová, Barbora ; Jurečková, Jana (referee) ; Hušková, Marie (advisor)
There are many test statistics that are based on U-statistics. This thesis deals with tests based on U-statistics for the general two-sample problem. After describing two-sample tests based on U-statistics from a general viewpoint, a presentation of some particular test statistics follows. All considered test statistics are described in a connection to the theory of U-statistics, with emphasis on their asymptotic properties. Special concern is given to tests based on a difference between two one-sample U-statistics and to tests based on empirical characteristic functions. Test statistics, based on a difference of two empirical characteristic functions, have a form of a V -statistic. A related U-statistic is derived and its properties are studied. An example of applying the bootstrap method to these test statistics is included.
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