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The Method of Dense Cycle Conditioni...

Banerjee, Debapratim.

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The Method of Dense Cycle Conditioning, Its Application, Computation and a Result on Concentration.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	The Method of Dense Cycle Conditioning, Its Application, Computation and a Result on Concentration./
作者:	Banerjee, Debapratim.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2019,
面頁冊數:	283 p.
附註:	Source: Dissertations Abstracts International, Volume: 81-04, Section: B.
Contained By:	Dissertations Abstracts International81-04B.
標題:	Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=22589527
ISBN:	9781088373347

The Method of Dense Cycle Conditioning, Its Application, Computation and a Result on Concentration.
Banerjee, Debapratim.

The Method of Dense Cycle Conditioning, Its Application, Computation and a Result on Concentration. - Ann Arbor : ProQuest Dissertations & Theses, 2019 - 283 p.

Source: Dissertations Abstracts International, Volume: 81-04, Section: B.

Thesis (Ph.D.)--University of Pennsylvania, 2019.

This item must not be sold to any third party vendors.

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.

ISBN: 9781088373347Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Dense cycle conditioning

The Method of Dense Cycle Conditioning, Its Application, Computation and a Result on Concentration.
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500 $a Source: Dissertations Abstracts International, Volume: 81-04, Section: B.
500 $a Advisor: Ma, Zongming.
502 $a Thesis (Ph.D.)--University of Pennsylvania, 2019.
506 $a This item must not be sold to any third party vendors.
520 $a 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.
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