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Large Number of Rare Events: Diversity Analysis in Multiple Choice Questionnaires and Related Topics

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posted on 2021-11-10, 07:43 authored by Kvizhinadze, Giorgi

The statistical analysis of a large number of rare events, (LNRE), which can also be called statistical theory of diversity, is the subject of acute interest both in statistical theory and in numerous applications. A careful eye will quickly see the presence of a large number of very rare objects almost everywhere: large numbers of rare species in ecosystems, large numbers of rare opinions in any opinion pool, large numbers of small admixtures in any solution and large numbers of rare words in any text are only few examples. In studying such objects, the interest for mathematical statisticians lies in the fact that most of the frequencies are small and, therefore, difficult to deal with. It is not immediately clear how one should be able to derive consistent and reliable inference from a large number of such frequencies. In this thesis we study the diversity of questionnaires with multiple answers. It has been demonstrated that this is a particular model of LNRE theory. In our analysis, the theories of large deviation, contiguity and Edgeworth expansion were employed, and limit theorems have been established.

History

Copyright Date

2010-01-01

Date of Award

2010-01-01

Publisher

Te Herenga Waka—Victoria University of Wellington

Rights License

Author Retains Copyright

Degree Discipline

Statistics

Degree Grantor

Te Herenga Waka—Victoria University of Wellington

Degree Level

Doctoral

Degree Name

Doctor of Philosophy

Victoria University of Wellington Item Type

Awarded Doctoral Thesis

Language

en_NZ

Victoria University of Wellington School

School of Mathematics, Statistics and Operations Research

Advisors

Khmaladze, Estate