LEADER 05588nam 2200541 450 001 996466403603316 005 20230427135836.0 010 $a3-030-80964-1 035 $a(CKB)4100000012024531 035 $a(MiAaPQ)EBC6721760 035 $a(Au-PeEL)EBL6721760 035 $a(OCoLC)1267762347 035 $a(PPN)258054735 035 $a(EXLCZ)994100000012024531 100 $a20220614d2021 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aConcentration of maxima and fundamental limits in high-dimensional testing and inference /$fZheng Gao, Stilian Stoev 210 1$aCham, Switzerland :$cSpringer International Publishing,$d[2021] 210 4$d©2021 215 $a1 online resource (147 pages) 225 1 $aSpringer Briefs in Probability and Mathematical Statistics 311 $a3-030-80963-3 327 $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 -- 3.1 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 -- 4.4 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 -- 6 Uniform Relative Stability for Gaussian Arrays. 327 $a6.1 Ramsey's Theory and the Structure of Correlation Matrices -- 6.2 URS Implies UDD (Proof of the ``Only If'' Part of Theorem6.1) -- 6.3 UDD Implies URS (Proof of the `If' Part of Theorem6.1) -- 6.3.1 Bounding the Upper Tails of AGG Maxima -- 6.3.2 Bounding the Lower Tails of Gaussian Maxima -- 6.4 Numerical Illustrations of Exact Support Recovery Under Dependence -- 7 Fundamental Statistical Limits in Genome-Wide Association Studies -- 7.1 Support Recovery Problems in Chi-Squared Models -- 7.1.1 The Exact Support Recovery Problem -- 7.1.2 The Exact-Approximate Support Recovery Problem -- 7.1.3 The Approximate Support Recovery Problem -- 7.1.4 The Approximate-Exact Support Recovery Problem -- 7.1.5 Comparison of One- Versus Two-Sided Alternatives in Additive Error Models -- 7.2 Odds Ratios and Statistical Power -- 7.3 Optimal Study Designs and Rare Variants -- 7.4 Phase Transitions in Large-Scale Association Screening Studies -- 7.5 Numerical Illustrations of the Phase Transitions in Chi-Square Models -- 7.5.1 Exact Support Recovery -- 7.5.2 Approximate, and Approximate-Exact Support Recovery -- Appendix A Additional Proofs -- A.1 Auxiliary Facts of Chi-Square Distributions -- A.2 Proof of Theorem7.1????eflinkthm:chispssquaredspsexactspsboundary7.17 -- A.3 Proof of Theorem7.3????eflinkthm:chispssquaredspsapproxspsboundary7.37 -- A.4 Proof of Theorems7.2????eflinkthm:chispssquaredspsexactspsapproxspsboundary7.27 and 7.4????eflinkthm:chispssquaredspsapproxspsexactspsboundary7.47 -- Appendix B Exact Support Recovery in Non AGG Models -- B.1 Strong Classification Boundaries in Other Light-Tailed Error Models -- B.1.1 Additive Error Models with Heavier-Than-AGG Tails -- B.1.2 Additive Error Models with Lighter-Than-AGG Tails -- B.2 Thresholding Procedures Under Heavy-Tailed Errors -- Appendix Bibliography. 410 0$aSpringer briefs in probability and mathematical statistics. 606 $aPhase transformations (Statistical physics) 606 $aPhase transformations (Statistical physics)$xData processing 606 $aMàxims i mínims$2thub 606 $aTransformacions de fase (Física estadística)$2thub 608 $aLlibres electrònics$2thub 615 0$aPhase transformations (Statistical physics) 615 0$aPhase transformations (Statistical physics)$xData processing. 615 7$aMàxims i mínims 615 7$aTransformacions de fase (Física estadística) 676 $a530.474 700 $aGao$b Zheng$0848991 702 $aStoev$b Stilian 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466403603316 996 $aConcentration of maxima and fundamental limits in high-dimensional testing and inference$92880204 997 $aUNISA LEADER 00660nam0-2200253---450 001 9910985495503321 005 20250319104004.0 100 $a20250318d1860----km-y0itay50------ba 101 0 $aita 102 $aIT 105 $ay-------001yy 200 1 $aSugl'innesti$ediscorso$fdi Francesco Feniziani 210 $aNapoli$cStamperia del Fibreno$d1860 215 $a64 p.$d17 cm 610 0 $aInnesto 676 $a631.541$v20$zita 700 1$aFeniziani,$bFrancesco$01792301 801 0$aIT$bUNINA$gREICAT$2UNIMARC 901 $aBK 912 $a9910985495503321 952 $aP V 35 (1$fDBV 959 $aDBV 996 $aSugl'innesti$94330760 997 $aUNINA LEADER 01022nam0 22002651i 450 001 UON00132409 005 20231205102801.957 100 $a20020107d1965 |0itac50 ba 101 $aben 102 $aIN 105 $a|||| 1|||| 200 1 $aMadhyaratera gana$fMahashveta Bhattacharya 210 $aKalikata$cVishvasa Pablishin$d1965 215 $a255 p.$d23 cm 606 $aLetteratura bengali$xNarrativa$3UONC030997$2FI 620 $aIN$dCalcutta$3UONL000111 686 $aSI VI ECX$cSUBCONT. INDIANO - LETTERATURA BENGALI - PERIODO MODERNO - TESTI$2A 700 1$aBHATTACHARYA$bMahashveta$3UONV080386$0668724 712 $aVishvasa Pablishin$3UONV262964$4650 801 $aIT$bSOL$c20251024$gRICA 899 $aSIBA - SISTEMA BIBLIOTECARIO DI ATENEO$2UONSI 912 $aUON00132409 950 $aSIBA - SISTEMA BIBLIOTECARIO DI ATENEO$dSI SI VI ECX 851 $eSI SA 60373 5 851 996 $aMadhyaratera gana$91314150 997 $aUNIOR