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master's thesis
U-statistike i primjene
2016. urn:nbn:hr:126:355136
Brdarić, Nikolina
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics and Mathematics Teaching
Probability, Mathematical Statistics and Data Science Research Group

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Brdarić, N. (2016). U-statistike i primjene (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:355136

Brdarić, Nikolina. "U-statistike i primjene." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2016. https://urn.nsk.hr/urn:nbn:hr:126:355136

Brdarić, Nikolina. "U-statistike i primjene." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2016. https://urn.nsk.hr/urn:nbn:hr:126:355136

Brdarić, N. (2016). 'U-statistike i primjene', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 10 November 2024, https://urn.nsk.hr/urn:nbn:hr:126:355136

Brdarić N. U-statistike i primjene [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2016 [cited 2024 November 10] Available at: https://urn.nsk.hr/urn:nbn:hr:126:355136

N. Brdarić, "U-statistike i primjene", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2016. Available at: https://urn.nsk.hr/urn:nbn:hr:126:355136

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Metadata
TitleU-statistike i primjene
Title (english)U-statistics and application
AuthorNikolina Brdarić
MentorMirta Benšić (mentor)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Pure Mathematics and Mathematics Teaching)
(Probability, Mathematical Statistics and Data Science Research Group)
Osijek
Defense date and country2016, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Probability Theory and Statistics
Abstract
Cilj ovog diplomskog rada bilo je upoznavanje s pojmom U-statistike kao nepristranog procjenitelja statistickog funkcionala očekivanja. Poseban naglasak stavljen je na primjenu U-statistika i njihovih svojstava. U radu su navedeni primjeri U-statistika koje se najčešće koriste pri procjeni parametara koje možemo zapisati pomoću funkcionala očekivanja. Također, dokazani su važni teoremi o varijanci i asimptotskoj varijanci U-statistika kao i teorem o njihovoj asimptotskoj normalnosti. U svrhu demonstriranje primjene U-statistika, obrađžen je Wilcoxonov test ranga i predznaka, teorijski i primjerom. Budući da se pokazalo kako asimptotska distribucija test-statistike Wilcoxonovog testa ranga i predznaka odgovara asimptotskoj distribuciji odrežene U-statistike, iskoristili smo ranije dokazana svojstva U -statistika kako bismo pokazali asimptotsku normalnost test-statistike Wilcoxonovog testa ranga i predznaka.
Abstract (english)
The aim of this thesis was to introduce the concept of U-statistics as unbiased estimators of statistical expectation functionals. Special emphasis was put on the application and properties of U-statistics. Further in the thesis, several examples of U-statistics which are used in the assessment of parameters that can be represented by using expectation functionals were given. Additionally, important theorems regarding variance, asymptotic variance as well as asymptotic normality of U-statistics have been proven. In order to demonstrate the application of the u-statistics, Wilcoxon signed rank test was explained in detail, both theoretically and by example. Since asymptotic distribution of Wilcoxon signed rank teststatistics corresponds to the asymptotic distribution of a specific U-statistics, properties of U-statistics were used to show asymptotic normality of Wilcoxon signed rank test-statistics.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:355136
Study programmeTitle: Mathematics; specializations in: Financial and Statistical Mathematics, Mathematics and Computer Science, Industrial and Applied Mathematics
Course: Financial and Statistical Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2016-04-07 07:49:18