Asimptotska razdioba statistika baziranih na rangovima

master's thesis

• Author: Ena Jurilj
• Mentor: Miljenko Huzak (mentor)
• Committee member: Miljenko Huzak (predsjednik povjerenstva)
• Committee member: Nikola Sarapa (član povjerenstva)
• Committee member: Siniša Slijepčević (član povjerenstva)
• Committee member: Tina Bosner (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2015-11-26, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U prvom se poglavlju prisjećamo osnovnih tipova konvergencija slučajnih varijabli. Navodimo nekoliko novih tvrdnji od kojih neke i dokazujemo. U drugom poglavlju iskazujemo Lindeberg-Fellerov centralni granični teorem i primjenjujemo ga direktno na neke statistike. Ovdje također iznosimo neke primjere koji koriste statistike koje zadovoljavaju Lindebergov uvjet. Glavni rezultat obradujemo u trećem poglavlju. Iskazujemo i dokazujemo posebnu verziju Lindeberg-Fellerova teorema za statistike bazirane na rangovima. U posljednjem poglavlju primjenjujemo prethodni teorem na statistike koje se pojavljuju u nekim neparametarskim metodama, kao npr. statistika kod permutacijskog t-testa dva uzorka, statistika kod testa sume rangova, itd.

Abstract (english)

In the first chapter we recall to basic types of convergences of random variables. Here we state a few claims about convergences, some of them with their proofs. In the second chapter we state Lindeberg-Feller Central Limit Theorem without proof. Then we apply it directly on some statistics. We also state some interesting examples that use statistics satisfying Lindeberg Condition. The main result is in the third chapter. There we state a special version of Lindeberg-Feller Theorem for the statistics based on ranks, with its proof. In the last chapter we apply this theorem to statistics that we use in some nonparametric methods, such as statistic for the Two-Sample Randomisation t-Test, or statistic for the Rank-Sum Test, etc.

• Keywords: konvergecija slučajnih varijabli; Lindeberg-Fellerov centralni granični teorem; permutacijski t-test dva uzorka; test sume rangova
• Keywords (english): convergence of random variables; Lindeberg-Feller Central Limit Theorem; Two-Sample Randomisation t-Test; Rank-Sum Test
• Language: croatian
• URN:NBN: urn:nbn:hr:217:140399
• Study programme: Title: Mathematical Statistics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-02-04 09:49:16