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Optimal Inference With a Multidimensional Multiscale Statistic- [electronic resource]
![Optimal Inference With a Multidimensional Multiscale Statistic - [electronic resource]](/Users/Baul/Images/book.png)
Optimal Inference With a Multidimensional Multiscale Statistic- [electronic resource]
상세정보
- 자료유형
- 학위논문파일 국외
- 최종처리일시
- 20240214101920
- ISBN
- 9798380593229
- DDC
- 310
- 서명/저자
- Optimal Inference With a Multidimensional Multiscale Statistic - [electronic resource]
- 발행사항
- [S.l.]: : Columbia University., 2023
- 발행사항
- Ann Arbor : : ProQuest Dissertations & Theses,, 2023
- 형태사항
- 1 online resource(124 p.)
- 주기사항
- Source: Dissertations Abstracts International, Volume: 85-04, Section: B.
- 주기사항
- Advisor: Sen, Bodhisattva;Zheng, Tian.
- 학위논문주기
- Thesis (Ph.D.)--Columbia University, 2023.
- 사용제한주기
- This item must not be sold to any third party vendors.
- 초록/해제
- 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.
- 일반주제명
- Statistics.
- 일반주제명
- Theoretical mathematics.
- 일반주제명
- Applied mathematics.
- 키워드
- Confidence bands
- 기타저자
- Columbia University Statistics
- 기본자료저록
- Dissertations Abstracts International. 85-04B.
- 기본자료저록
- Dissertation Abstract International
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■00520240214101920
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■007cr#unu||||||||
■020 ▼a9798380593229
■035 ▼a(MiAaPQ)AAI30689925
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a310
■1001 ▼aDatta, Pratyay Ashley.
■24510▼aOptimal Inference With a Multidimensional Multiscale Statistic▼h[electronic resource]
■260 ▼a[S.l.]:▼bColumbia University. ▼c2023
■260 1▼aAnn Arbor :▼bProQuest Dissertations & Theses, ▼c2023
■300 ▼a1 online resource(124 p.)
■500 ▼aSource: Dissertations Abstracts International, Volume: 85-04, Section: B.
■500 ▼aAdvisor: Sen, Bodhisattva;Zheng, Tian.
■5021 ▼aThesis (Ph.D.)--Columbia University, 2023.
■506 ▼aThis item must not be sold to any third party vendors.
■520 ▼aWe 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.
■590 ▼aSchool code: 0054.
■650 4▼aStatistics.
■650 4▼aTheoretical mathematics.
■650 4▼aApplied mathematics.
■653 ▼aConfidence bands
■653 ▼aMultidimensional optimal inference
■653 ▼aMultiscale statistics
■653 ▼aShape restricted regression
■690 ▼a0463
■690 ▼a0642
■690 ▼a0364
■71020▼aColumbia University▼bStatistics.
■7730 ▼tDissertations Abstracts International▼g85-04B.
■773 ▼tDissertation Abstract International
■790 ▼a0054
■791 ▼aPh.D.
■792 ▼a2023
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T16935336▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
■980 ▼a202402▼f2024
