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Connections among multivariate rank ...

Wang, Yunfei.

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Connections among multivariate rank functions, depth functions, and sign and signed-rank statistics.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Connections among multivariate rank functions, depth functions, and sign and signed-rank statistics./
作者:	Wang, Yunfei.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2016,
面頁冊數:	98 p.
附註:	Source: Dissertations Abstracts International, Volume: 78-03, Section: B.
Contained By:	Dissertations Abstracts International78-03B.
標題:	Statistics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10151456
ISBN:	9781369062205

Connections among multivariate rank functions, depth functions, and sign and signed-rank statistics.
Wang, Yunfei.

Connections among multivariate rank functions, depth functions, and sign and signed-rank statistics. - Ann Arbor : ProQuest Dissertations & Theses, 2016 - 98 p.

Source: Dissertations Abstracts International, Volume: 78-03, Section: B.

Thesis (Ph.D.)--The University of Texas at Dallas, 2016.

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

In the multivariate data setting, depth, outlyingness, quantile and rank functions describe a distribution or data set from different perspectives (Serfing, 2010). There is an abundance of formulations of these types of functions, but no particular versions have been adopted as "best". The interrelations among the depth, outlyingness, quantile and rank functions have been investigated and formulated as a "Depth-Outlyingness-Quantile-Rank (DOQR) Paradigm" (Serfing, 2010). The DOQR paradigm clarifies the equivalence between the four notions and serves as a guideline for introducing new depth, outlyingness, quantile and rank functions. This dissertation clarifies the definitions and formulations of depth, outlyingness, quantile and rank functions, develops more complete and precise connections among these functions and related sign and signed-rank test statistics, and exploits these connections to suggest and investigate some new depth and rank functions. Firstly, depth, outlyingness, quantile and rank functions are reviewed and characterized through desirable properties. Secondly, the DOQR paradigm is updated with respect to the affine equivariance condition for quantile and rank functions. Thirdly, two important applications of the DOQR paradigm are discussed. (i) The theory on generation of rank functions by depth and outlyingness functions is enriched, with three scenarios discussed in detail and several new depth, outlyingness and rank functions defined. (ii) The generation of depth and outlyingness functions from rank functions is illustrated by formulating new "Hodges-Lehmann" type depth functions, and a special case, Hodges-Lehmann projection depth function, is found to have nice performance and deserve a recommendation. Fourthly, a novel interdirections depth function is derived from the well-known interdirections sign test (Randles, 1989), and its properties are studied using U-statistic theory. Finally, surprising connections between the interdirections depth function and the simplicial depth function (Liu, 1988, 1990) are established, simulation studies are carried out, and the applications of the connections are discussed. In Chapter 2, various preliminaries are covered. In Chapter 3, depth, outlyingness, quantile and rank functions are introduced and characterized, examples are given, and relevant affine invariance and equivariance properties are discussed. The DOQR paradigm describing their connections is developed in detail. Chapter 4 discusses the two applications of the DOQR paradigm. In Chapter 5, the interdirections sign test is revisited and the interdirections depth function is introduced and studied. In Chapter 6, connections between the interdirections depth function and the simplicial depth function are discussed. Chapter 7 summarizes selected directions for further work.

ISBN: 9781369062205Subjects--Topical Terms:

517247
Statistics.
Subjects--Index Terms:

DOQR paradigm

Connections among multivariate rank functions, depth functions, and sign and signed-rank statistics.
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300 $a 98 p.
500 $a Source: Dissertations Abstracts International, Volume: 78-03, Section: B.
500 $a Publisher info.: Dissertation/Thesis.
500 $a Advisor: Serfling, Robert.
502 $a Thesis (Ph.D.)--The University of Texas at Dallas, 2016.
506 $a This item must not be sold to any third party vendors.
520 $a In the multivariate data setting, depth, outlyingness, quantile and rank functions describe a distribution or data set from different perspectives (Serfing, 2010). There is an abundance of formulations of these types of functions, but no particular versions have been adopted as "best". The interrelations among the depth, outlyingness, quantile and rank functions have been investigated and formulated as a "Depth-Outlyingness-Quantile-Rank (DOQR) Paradigm" (Serfing, 2010). The DOQR paradigm clarifies the equivalence between the four notions and serves as a guideline for introducing new depth, outlyingness, quantile and rank functions. This dissertation clarifies the definitions and formulations of depth, outlyingness, quantile and rank functions, develops more complete and precise connections among these functions and related sign and signed-rank test statistics, and exploits these connections to suggest and investigate some new depth and rank functions. Firstly, depth, outlyingness, quantile and rank functions are reviewed and characterized through desirable properties. Secondly, the DOQR paradigm is updated with respect to the affine equivariance condition for quantile and rank functions. Thirdly, two important applications of the DOQR paradigm are discussed. (i) The theory on generation of rank functions by depth and outlyingness functions is enriched, with three scenarios discussed in detail and several new depth, outlyingness and rank functions defined. (ii) The generation of depth and outlyingness functions from rank functions is illustrated by formulating new "Hodges-Lehmann" type depth functions, and a special case, Hodges-Lehmann projection depth function, is found to have nice performance and deserve a recommendation. Fourthly, a novel interdirections depth function is derived from the well-known interdirections sign test (Randles, 1989), and its properties are studied using U-statistic theory. Finally, surprising connections between the interdirections depth function and the simplicial depth function (Liu, 1988, 1990) are established, simulation studies are carried out, and the applications of the connections are discussed. In Chapter 2, various preliminaries are covered. In Chapter 3, depth, outlyingness, quantile and rank functions are introduced and characterized, examples are given, and relevant affine invariance and equivariance properties are discussed. The DOQR paradigm describing their connections is developed in detail. Chapter 4 discusses the two applications of the DOQR paradigm. In Chapter 5, the interdirections sign test is revisited and the interdirections depth function is introduced and studied. In Chapter 6, connections between the interdirections depth function and the simplicial depth function are discussed. Chapter 7 summarizes selected directions for further work.
590 $a School code: 0382.
650 4 $a Statistics. $3 517247
653 $a DOQR paradigm
653 $a Depth functions
653 $a Outlyingness functions
653 $a Quantile functions
653 $a Rank functions
653 $a Sign and signed-rank test statistics
690 $a 0463
710 2 $a The University of Texas at Dallas. $b Statistics. $3 3429061
773 0 $t Dissertations Abstracts International $g 78-03B.
790 $a 0382
791 $a Ph.D.
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793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10151456