자료유형  

 학위논문

Control Number  

0015490823

International Standard Book Number  

9781085560696

Dewey Decimal Classification Number  

004

Main Entry-Personal Name  

Zhang, Linjun.

Publication, Distribution, etc. (Imprint  

[Sl] : University of Pennsylvania, 2019

Publication, Distribution, etc. (Imprint  

Ann Arbor : ProQuest Dissertations & Theses, 2019

Physical Description  

199 p

General Note  

Source: Dissertations Abstracts International, Volume: 81-02, Section: B.

General Note  

Advisor: Cai, T. Tony.

Dissertation Note  

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

Restrictions on Access Note  

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

Summary, Etc.  

요약The age of "Big Data" features large volume of massive and high-dimensional datasets, leading to fast emergence of different algorithms, as well as new concerns such as privacy and fairness. To compare different algorithms with (without) these new constraints, minimax decision theory provides a principled framework to quantify the optimality of algorithms and investigate the fundamental difficulty of statistical problems. Under the framework of minimax theory, this thesis aims to address the following four problems: 1. The first part of this thesis aims to develop an optimality theory for linear discriminant analysis in the high-dimensional setting. In addition, we consider classification with incomplete data under the missing completely at random (MCR) model. 2. In the second part, we study high-dimensional sparse Quadratic Discriminant Analysis (QDA) and aim to establish the optimal convergence rates. 3. In the third part, we study the optimality of high-dimensional clustering on the unsupervised setting under the Gaussian mixtures model. We propose a EM-based procedure with the optimal rate of convergence for the excess mis-clustering error. 4. In the fourth part, we investigate the minimax optimality under the privacy constraint for mean estimation and linear regression models, under both the classical low-dimensional and modern high-dimensional settings.

Subject Added Entry-Topical Term  

Statistics

Subject Added Entry-Topical Term  

Computer science

Added Entry-Corporate Name  

University of Pennsylvania Statistics

Host Item Entry  

Dissertations Abstracts International. 81-02B.

Host Item Entry  

Dissertation Abstract International

Electronic Location and Access  

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Control Number  

joongbu:566923