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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.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Contributions to the Theory and Applications of Statistical Distances./
作者:	Chen, Yang.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2018,
面頁冊數:	194 p.
附註:	Source: Dissertation Abstracts International, Volume: 79-08(E), Section: B.
Contained By:	Dissertation Abstracts International79-08B(E).
標題:	Biostatistics. -
電子資源:	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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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.
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