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The Method of Dense Cycle Conditioning, Its Application, Computation and a Result on Concentration
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| 자료유형 | 학위논문 |
|---|---|
| 서명/저자사항 | The Method of Dense Cycle Conditioning, Its Application, Computation and a Result on Concentration. |
| 개인저자 | Banerjee, Debapratim. |
| 단체저자명 | University of Pennsylvania. Statistics. |
| 발행사항 | [S.l.]: University of Pennsylvania., 2019. |
| 발행사항 | Ann Arbor: ProQuest Dissertations & Theses, 2019. |
| 형태사항 | 283 p. |
| 기본자료 저록 | Dissertations Abstracts International 81-04B. Dissertation Abstract International |
| ISBN | 9781088373347 |
| 학위논문주기 | Thesis (Ph.D.)--University of Pennsylvania, 2019. |
| 일반주기 |
Source: Dissertations Abstracts International, Volume: 81-04, Section: B.
Advisor: Ma, Zongming. |
| 이용제한사항 | This item must not be sold to any third party vendors. |
| 요약 | This dissertation contains works on three different directions. In the first direction, three different problems have been solved. The fundamental theme of these problems are to consider the log-likelihood ratio of certain processes under local perturbations. It is shown that in these cases below certain threshold the log-likelihood ratio can be approximated by log-likelihood ratio restricted to a certain class of statistics called the ``signed cycles". These statistics were considered by the author in order to study contiguity for planted partition model in dense case. Details are given in Chapter 2. The sparse case is known in the literature by a paper of Mossel et al. These statistics found further applications in statistics and statistical physics where two other problems were solved. One might look at Chapters 3 and 1 for details. The second direction of this thesis is to show computability of these cycle statistics. It is proved that the ``signed cycles" statistics can be approximated by certain linear spectral statistics of high dimensional random matrices. The proof techniques are highly motivated by a paper of Anderson and Zeitouni. One can have a look at Chapter 4 for details. In the third direction a problem of concentration inequality is considered. A Bernstein type concentration inequality is proved for statistics which are generalizations of a statistics introduced by Hoeffding. It is proven using the method exchangeable pairs introduced by Chatterjee. One might look at Chapter 6 for details. |
| 일반주제명 | Mathematics. Statistics. Statistical physics. |
| 언어 | 영어 |
| 바로가기 | 
: 이 자료의 원문은 한국교육학술정보원에서 제공합니다. |
