자료유형  

 학위논문

Control Number  

0016935336

International Standard Book Number  

9798380593229

Dewey Decimal Classification Number  

310

Main Entry-Personal Name  

Datta, Pratyay Ashley.

Publication, Distribution, etc. (Imprint  

[S.l.] : Columbia University., 2023

Publication, Distribution, etc. (Imprint  

Ann Arbor : ProQuest Dissertations & Theses, 2023

Physical Description  

1 online resource(124 p.)

General Note  

Source: Dissertations Abstracts International, Volume: 85-04, Section: B.

General Note  

Advisor: Sen, Bodhisattva;Zheng, Tian.

Dissertation Note  

Thesis (Ph.D.)--Columbia University, 2023.

Restrictions on Access Note  

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

Summary, Etc.  

요약We observe a stochastic process Y on [0,1]d (d ≥ 1) satisfying dY(t)=n1/2f(t)dt + dW(t), t ∈ [0,1]d, where n ≥ 1 is a given scale parameter (`sample size'), W is the standard Brownian sheet on [0,1]d and f ∈ L1([0,1]d) is the unknown function of interest. We propose a multivariate multiscale statistic in this setting and prove that the statistic attains a subexponential tail bound; this extends the work of 'Dumbgen and Spokoiny (2001)' who proposed the analogous statistic for d = 1. In the process, we generalize Theorem 6.1 of 'Dumbgen and Spokoiny (2001)' about stochastic processes with sub-Gaussian increments on a pseudometric space, which is of independent interest. We use the proposed multiscale statistic to construct optimal tests (in an asymptotic minimax sense) for testing f = 0 versus (i) appropriate Holder classes of functions, and (ii) alternatives of the form f = μn IBn, where Bn is an axis-aligned hyperrectangle in [0,1]d and μn ∈ R; μn and Bn unknown. In Chapter 3 we use this proposed multiscale statistics to construct honest confidence bands for multivariate shape-restricted regression including monotone and convex functions.

Subject Added Entry-Topical Term  

Statistics.

Subject Added Entry-Topical Term  

Theoretical mathematics.

Subject Added Entry-Topical Term  

Applied mathematics.

Index Term-Uncontrolled  

Confidence bands

Index Term-Uncontrolled  

Multidimensional optimal inference

Index Term-Uncontrolled  

Multiscale statistics

Index Term-Uncontrolled  

Shape restricted regression

Added Entry-Corporate Name  

Columbia University Statistics

Host Item Entry  

Dissertations Abstracts International. 85-04B.

Host Item Entry  

Dissertation Abstract International

Electronic Location and Access  

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Control Number  

joongbu:639323