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001439573 001__ 1439573
001439573 003__ OCoLC
001439573 005__ 20230309004435.0
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001439573 019__ $$a1267686767
001439573 020__ $$a9783030809645$$q(electronic bk.)
001439573 020__ $$a3030809641$$q(electronic bk.)
001439573 020__ $$z3030809633
001439573 020__ $$z9783030809638
001439573 0247_ $$a10.1007/978-3-030-80964-5$$2doi
001439573 035__ $$aSP(OCoLC)1267762347
001439573 040__ $$aEBLCP$$beng$$epn$$cEBLCP$$dYDX$$dGW5XE$$dOCLCO$$dEBLCP$$dOCLCF$$dOCLCQ$$dCOM$$dOCLCO$$dN$T$$dSFB$$dOCLCQ
001439573 049__ $$aISEA
001439573 050_4 $$aQA402.5
001439573 08204 $$a511/.66$$223
001439573 1001_ $$aGao, Zheng.
001439573 24510 $$aConcentration of maxima and fundamental limits in high-dimensional testing and inference /$$cZheng Gao, Stilian Stoev.
001439573 260__ $$aCham :$$bSpringer,$$c2021.
001439573 300__ $$a1 online resource (147 pages)
001439573 336__ $$atext$$btxt$$2rdacontent
001439573 337__ $$acomputer$$bc$$2rdamedia
001439573 338__ $$aonline resource$$bcr$$2rdacarrier
001439573 4901_ $$aSpringerBriefs in Probability and Mathematical Statistics
001439573 500__ $$aA.1 Auxiliary Facts of Chi-Square Distributions.
001439573 504__ $$aIncludes bibliographical references.
001439573 5050_ $$aIntro -- Preface -- Contents -- Acronyms -- 1 Introduction and Guiding Examples -- 1.1 The Additive Error Model -- 1.2 Genome-Wide Association Studies and the Chi-Square Model -- 1.3 Contents -- 2 Risks, Procedures, and Error Models -- 2.1 Statistical Risks -- 2.2 Statistical Procedures -- 2.3 Related Literature and Our Contributions -- 2.4 Relationships Between the Asymptotic Risks -- 2.5 The Asymptotic Generalized Gaussian (AGG) Models -- 2.6 Rapid Variation and Relative Stability -- 2.7 Auxiliary Facts About Gaussian Distributions -- 3 A Panorama of Phase Transitions
001439573 5058_ $$a3.1 Sparse Signal Detection Problems -- 3.2 Sparse Signal Support Recovery Problems -- 3.3 The Exact Support Recovery Problem -- 3.4 The Approximate Support Recovery Problem -- 3.5 Monotonicity of the Benjamini-Hochberg Procedure -- 3.6 The Exact-Approximate Support Recovery Problem -- 3.7 The Approximate-Exact Support Recovery Problem -- 3.8 Asymptotic Power Analysis: A Discussion -- 4 Exact Support Recovery Under Dependence -- 4.1 Generalizations of Distributional and Dependence Assumptions -- 4.2 Sufficient Conditions for Exact Support Recovery -- 4.3 Dependence and Uniform Relative Stability
001439573 5058_ $$a4.4 Necessary Conditions for Exact Support Recovery -- 4.5 Dense Signals -- 4.6 Numerical Illustrations for Independent Errors -- 5 Bayes and Minimax Optimality -- 5.1 Bayes Optimality in Support Recovery Problems -- 5.2 Bayes Optimality of Oracle Thresholding -- 5.3 Bayes Optimality of Likelihood Ratio Thresholding -- 5.4 Sub-optimality of Data Thresholding Procedures -- 5.5 Minimax Optimality in Exact Support Recovery -- 5.5.1 Point-Wise Minimax Optimality for Thresholding Procedures -- 5.5.2 Minimax Optimality over All Procedures -- 5.6 Optimality and Sub-optimality: A Discussion
001439573 5058_ $$a6 Uniform Relative Stability for Gaussian Arrays -- 6.1 Ramsey's Theory and the Structure of Correlation Matrices -- 6.2 URS Implies UDD (Proof of the ``Only If'' Part of Theorem6.1) -- 6.3 UDD Implies URS (Proof of the `If' Part of Theorem6.1) -- 6.3.1 Bounding the Upper Tails of AGG Maxima -- 6.3.2 Bounding the Lower Tails of Gaussian Maxima -- 6.4 Numerical Illustrations of Exact Support Recovery Under Dependence -- 7 Fundamental Statistical Limits in Genome-Wide Association Studies -- 7.1 Support Recovery Problems in Chi-Squared Models -- 7.1.1 The Exact Support Recovery Problem
001439573 5058_ $$a7.1.2 The Exact-Approximate Support Recovery Problem -- 7.1.3 The Approximate Support Recovery Problem -- 7.1.4 The Approximate-Exact Support Recovery Problem -- 7.1.5 Comparison of One- Versus Two-Sided Alternatives in Additive Error Models -- 7.2 Odds Ratios and Statistical Power -- 7.3 Optimal Study Designs and Rare Variants -- 7.4 Phase Transitions in Large-Scale Association Screening Studies -- 7.5 Numerical Illustrations of the Phase Transitions in Chi-Square Models -- 7.5.1 Exact Support Recovery -- 7.5.2 Approximate, and Approximate-Exact Support Recovery -- Appendix A Additional Proofs
001439573 506__ $$aAccess limited to authorized users.
001439573 520__ $$aThis book provides a unified exposition of some fundamental theoretical problems in high-dimensional statistics. It specifically considers the canonical problems of detection and support estimation for sparse signals observed with noise. Novel phase-transition results are obtained for the signal support estimation problem under a variety of statistical risks. Based on a surprising connection to a concentration of maxima probabilistic phenomenon, the authors obtain a complete characterization of the exact support recovery problem for thresholding estimators under dependent errors.
001439573 588__ $$aDescription based on print version record.
001439573 650_0 $$aMaxima and minima.
001439573 650_0 $$aPhase transformations (Statistical physics)
001439573 650_6 $$aMaximums et minimums.
001439573 650_6 $$aTransitions de phase.
001439573 655_0 $$aElectronic books.
001439573 7001_ $$aStoev, Stilian.
001439573 77608 $$iPrint version:$$aGao, Zheng.$$tConcentration of Maxima and Fundamental Limits in High-Dimensional Testing and Inference.$$dCham : Springer International Publishing AG, ©2021$$z9783030809638
001439573 830_0 $$aSpringer briefs in probability and mathematical statistics.
001439573 852__ $$bebk
001439573 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-030-80964-5$$zOnline Access$$91397441.1
001439573 909CO $$ooai:library.usi.edu:1439573$$pGLOBAL_SET
001439573 980__ $$aBIB
001439573 980__ $$aEBOOK
001439573 982__ $$aEbook
001439573 983__ $$aOnline
001439573 994__ $$a92$$bISE