KARAKTERIZACIJE NEKIH RASPODELA I BAHADUROVA ASIMPTOTSKA EFIKASNOST TESTOVA SAGLASNOSTI

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KARAKTERIZACIJE NEKIH RASPODELA I BAHADUROVA ASIMPTOTSKA EFIKASNOST TESTOVA SAGLASNOSTI

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dc.contributor.advisor Janković, Slobodanka
dc.contributor.author Obradović, Marko
dc.date.accessioned 2016-09-01T07:57:06Z
dc.date.available 2016-09-01T07:57:06Z
dc.date.issued 2015
dc.identifier.uri http://hdl.handle.net/123456789/4288
dc.description.abstract First characterizations of probability distributions date to the thirties of last century. This area, which lies on the borderline of probability theory and mathematical statistics, attracts large number of researchers, and in recent times the number of papers on the subject is increasing. Goodness-of- t tests are among the most important nonparametric tests. Many of them are based on empirical distribution function. The application of characterization theorems for construction of goodness-of- t tests dates to the middle of last century, and recently has become one of the main directions in this eld. The advantage of such tests is that they are often free of distribution parametres and hence enable testing of composite hypotheses. The goals of this dissertation are the formulation of new characterizations of exponential and Pareto distribution, as well as the application of the theory of U-statistics, large deviations and Bahadur e ciency to construction and examination of asymptotics of goodness-of- t tests for aforementioned distributions. The dissertation consists of six chapters. In the rst chapter a review of di erent types of characterizations is presented, pointing out their abundance and variety. The special emphasis is given to the characterizations based on equidistribution of functions of the sample. Besides, two new characterizations of Pareto distribution are presented. The second chapter is devoted to some new characterizations of the exponential distributions presented in papers [65] and [53]. Six characterizations based on order statistics are presented. A special case of one of them (theorem 2.4.3) represents the solution of open problem stated by Arnold and Villasenor [9]. In the third chapter there are basic concepts on U-statistics, the class of statistics important in the theory of unbiased estimation. Some of their asymptotic properties are given. U-empirical distribution functions, a generalization of standard empirical distribution functions, are also de ned. The fourth chapter is dedicated to the asymptotic e ciency of statistical tests, primarily to Bahadur asymptotic e ciency, i.e. asymptotic e ciency of the test when the level of signi cance approaches zero. Some theoretical results from the monograph by Nikitin [57], and papers [61], [59], etc. are shown. In the fth chapter new results in the eld of goodness-of- t tests for Pareto distribution are presented. Based on three characterizations of Pareto distribution given in section 1.1.2. six goodness-of- t tests, three of integral, and three of Kolmogorov type, are proposed. In each case the composite null hypothesis is tested since the test statistics are free of the parameter of Pareto distribution. For each test the asymptotic distribution under null hypothesis, as well as asymptotic behaviour of the tail (large deviations) under close alternatives is derived. For some standard alternatives, the local Bahadur asymptotic e ciency is calculated and the domains of local asymptotic optimality are obtained. The results from this chapter are published in [66] and [64]. The sixth chapter brings new goodness-of- t tests for exponential distribution. Based on the solved hypothesis of Arnold and Villasenor two classes of tests, integral and Kolmogorov type, are proposed, depending on the number of summands in the characterization. The study of asymptotic properties, analogous to the ones in the fth chapter is done in case of two and three summands, for which the tests have practical importance. The results of this chapter are presented in [39]. en_US
dc.description.provenance Submitted by Slavisha Milisavljevic (slavisha) on 2016-09-01T07:57:06Z No. of bitstreams: 1 phdObradovicMarko.pdf: 789301 bytes, checksum: ec8227bd092c34c45226f2987ce79912 (MD5) en
dc.description.provenance Made available in DSpace on 2016-09-01T07:57:06Z (GMT). No. of bitstreams: 1 phdObradovicMarko.pdf: 789301 bytes, checksum: ec8227bd092c34c45226f2987ce79912 (MD5) Previous issue date: 2015 en
dc.language.iso sr en_US
dc.publisher Beograd en_US
dc.title KARAKTERIZACIJE NEKIH RASPODELA I BAHADUROVA ASIMPTOTSKA EFIKASNOST TESTOVA SAGLASNOSTI en_US
mf.author.birth-date 1978-12-24
mf.author.birth-place Kruševac en_US
mf.author.birth-country Srbija en_US
mf.author.residence-state Srbija en_US
mf.author.citizenship Srpsko en_US
mf.author.nationality Srbin en_US
mf.subject.area Mathematics en_US
mf.subject.keywords characterizations of probability distributions, exponential distribution, Pareto distribution, goodness-of- t tests, Bahadur e ciency, large deviation theory, U-statistics en_US
mf.subject.subarea Probability and Statistics en_US
mf.contributor.committee Jevremović, Vesna
mf.contributor.committee Nikitin, Jakov Jurjevič
mf.university.faculty Mathematical Faculty en_US
mf.document.references 89 en_US
mf.document.pages 130 en_US
mf.document.location Beograd en_US
mf.document.genealogy-project No en_US
mf.university Belgrade University en_US

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