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Contributions to the Theory and Appl...

Chen, Yang.

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Contributions to the Theory and Applications of Statistical Distances.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Contributions to the Theory and Applications of Statistical Distances./
Author:	Chen, Yang.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2018,
Description:	194 p.
Notes:	Source: Dissertation Abstracts International, Volume: 79-08(E), Section: B.
Contained By:	Dissertation Abstracts International79-08B(E).
Subject:	Biostatistics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10744955
ISBN:	9780355680188

Contributions to the Theory and Applications of Statistical Distances.
Chen, Yang.

Contributions to the Theory and Applications of Statistical Distances. - Ann Arbor : ProQuest Dissertations & Theses, 2018 - 194 p.

Source: Dissertation Abstracts International, Volume: 79-08(E), Section: B.

Thesis (Ph.D.)--State University of New York at Buffalo, 2018.

In this dissertation, we first study statistical distances that are either used extensively in practice or are of interest to use in model adequacy problems. We offer statistical interpretations of these distances and show how they could be obtained as solutions of certain optimization problems. Especially, generalized chi-squared distances arise as solutions to appropriately defined optimization problems with interpretable constraints. We also study the properties of non-quadratic distances such as the total variation distance and the mixture index of fit.

ISBN: 9780355680188Subjects--Topical Terms:

1002712
Biostatistics.

Contributions to the Theory and Applications of Statistical Distances.
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245 1 0 $a Contributions to the Theory and Applications of Statistical Distances.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2018
300 $a 194 p.
500 $a Source: Dissertation Abstracts International, Volume: 79-08(E), Section: B.
500 $a Adviser: Marianthi Markatou.
502 $a Thesis (Ph.D.)--State University of New York at Buffalo, 2018.
520 $a In this dissertation, we first study statistical distances that are either used extensively in practice or are of interest to use in model adequacy problems. We offer statistical interpretations of these distances and show how they could be obtained as solutions of certain optimization problems. Especially, generalized chi-squared distances arise as solutions to appropriately defined optimization problems with interpretable constraints. We also study the properties of non-quadratic distances such as the total variation distance and the mixture index of fit.
520 $a We then discuss the fundamental role of statistical distances in the problem of multivariate two-sample goodness-of-fit testing and review various existing multivariate two-sample goodness-of-fit tests from both statistics and machine learning literature. The critical analysis conducted for these existing tests delivers the fact that there does not exist a satisfactory multivariate two-sample goodness-of-fit test that exhibits appropriate level of significance and high power in the presence of large samples and relatively high dimensions. Therefore, we propose new multivariate two-sample goodness-of-fit tests based on the kernel-based quadratic distance. We investigate the asymptotic properties of the proposed tests and provide an algorithm to select the most appropriate kernel tuning parameter. Our simulation experiments indicate that the proposed tests are superior to all other existing tests in terms of achieved level and power. We also use real data to illustrate the practical implementation of the proposed tests and compare the proposed tests with the existing ones.
590 $a School code: 0656.
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710 2 $a State University of New York at Buffalo. $b Biostatistics. $3 2099967
773 0 $t Dissertation Abstracts International $g 79-08B(E).
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791 $a Ph.D.
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793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10744955