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Contributions to Statistical Methods...

Zhang, Xiang.

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Contributions to Statistical Methods for High Dimensional and Dependent Data.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Contributions to Statistical Methods for High Dimensional and Dependent Data./
作者:	Zhang, Xiang.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2016,
面頁冊數:	139 p.
附註:	Source: Dissertation Abstracts International, Volume: 78-08(E), Section: B.
Contained By:	Dissertation Abstracts International78-08B(E).
標題:	Statistics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10585489
ISBN:	9781369639674

Contributions to Statistical Methods for High Dimensional and Dependent Data.
Zhang, Xiang.

Contributions to Statistical Methods for High Dimensional and Dependent Data. - Ann Arbor : ProQuest Dissertations & Theses, 2016 - 139 p.

Source: Dissertation Abstracts International, Volume: 78-08(E), Section: B.

Thesis (Ph.D.)--North Carolina State University, 2016.

In this thesis, we develop three new statistical methods for high dimensional and dependent data. The three methods are motivated by three independent projects.

ISBN: 9781369639674Subjects--Topical Terms:

517247
Statistics.

Contributions to Statistical Methods for High Dimensional and Dependent Data.
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500 $a Source: Dissertation Abstracts International, Volume: 78-08(E), Section: B.
500 $a Adviser: Alyson Wilson.
502 $a Thesis (Ph.D.)--North Carolina State University, 2016.
520 $a In this thesis, we develop three new statistical methods for high dimensional and dependent data. The three methods are motivated by three independent projects.
520 $a In the first project, we investigate variable selection for support vector machines for high dimensional data. A general class of non-convex penalized support vector machines is proposed. We show that one of the local solutions to the non-convex penalized support vector machines is the oracle estimator. This is the first variable selection consistency result for support vector machines in high dimensions. We also present an algorithm with provable global convergence to the oracle estimator. Our proof techniques are novel and do not require the differentiability of the loss function, which extend the existing results in the literature where the loss function is restricted to be a smooth function.
520 $a In the second project, we study system reliability and component importance for dependent systems. We establish a unified and general framework to characterize the influence of a dependence structure on system reliability and component importance. Our results are based on recent developments for copula theory with discrete marginal distributions. We reveal the connections of system reliability and component importance under dependence to some well-known principles under independence assumption. We also extend our results to multi-state system. Our derived results are further demonstrated using a Gaussian copula, and we show that the effects of dependence under a Gaussian copula have simple interpretations.
520 $a In the third project, we propose a new method to conduct regression on longitudinal imaging data. The proposed method integrates tensor decomposition with generalized estimating equations. We exploit a low-rank tensor decomposition to reduce the high dimensionality of image covariates and use generalized estimating equations to capture the temporal dependence in the longitudinal data. This new approach is shown to possess desirable theoretical properties. We also provide the first rank selection consistency result in the literature under the framework of tensor regression.
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