LEADER 05893nam 2200529 450 001 9910484167603321 005 20230421121854.0 010 $a3-030-69009-1 035 $a(CKB)4100000011912103 035 $a(MiAaPQ)EBC6577315 035 $a(Au-PeEL)EBL6577315 035 $a(OCoLC)1249475123 035 $a(PPN)255295677 035 $a(EXLCZ)994100000011912103 100 $a20211210d2021 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 00$aFestschrift in honor of R. Dennis Cook $efifty years of contribution to statistical science /$fEfstathia Bura, Bing Li, editors 210 1$aCham, Switzerland :$cSpringer,$d[2021] 210 4$d©2021 215 $a1 online resource (200 pages) 311 $a3-030-69008-3 327 $aIntro -- Foreword -- A Tribute to Professor R. Dennis Cook -- Contents -- Using Mutual Information to Measure the Predictive Powerof Principal Components -- 1 Introduction -- 2 Overview of Previous Results -- 3 Conditional Mutual Information -- 3.1 Under the Linear Model -- 3.2 Beyond the Linear Regression Model -- 3.3 Beyond the Normal Distribution -- 4 Discussion -- References -- A Robust Estimation Approach for Mean-Shiftand Variance-Inflation Outliers -- 1 Introduction -- 2 Our Proposal and Some Background -- 2.1 A Generalized Setting -- 2.2 Some Technical Background -- 2.3 Our Proposal -- 2.4 Graphical Diagnostics -- 3 Simulation Study -- 4 Real-Data Examples -- 5 Final Remarks -- References -- Estimating Sufficient Dimension Reduction Spaces by Invariant Linear Operators -- 1 Introduction -- 2 Invariant Linear Operators -- 3 Invariant Linear Operator and Its Eigenvectors -- 4 Some Important Members of T Y|X -- 4.1 Sliced Average Variance Estimation -- 4.2 SIR-II -- 4.3 Contour Regression -- 4.4 Directional Regression -- 5 Two Estimation Methods Based on Invariant Operators -- 5.1 Iterative Invariant Transformations (IIT) -- 5.2 Nonparametrically Boosted Inverse Regression (NBIR) -- 6 Numerical Study -- 7 Concluding Remarks -- References -- Testing Model Utility for Single Index Models Under High Dimension -- 1 Introduction -- 2 Generalized SNR for Single Index Models -- 2.1 Notation -- 2.2 A Brief Review of the Sliced Inverse Regression (SIR) -- 2.3 Generalized Signal-to-Noise Ratio of Single Index Models -- 2.4 Global Testing for Single Index Models -- 3 The Optimal Test for Single Index Models -- 3.1 The Detection Boundary of Linear Regression -- 3.2 Single Index Models -- 3.3 Optimal Test for SIMa -- 3.4 Computationally Efficient Test -- 3.5 Practical Issues -- 4 Numerical Studies -- 5 Discussion -- Appendix: Proofs -- Assisting Lemmas. 327 $aProof of Theorems -- References -- Sliced Inverse Regression for Spatial Data -- 1 Introduction -- 2 SIR for iid Data -- 3 SIR for Time Series Data -- 4 SIR for Spatial Data -- 5 Performance Evaluation of SSIR -- 6 Discussion -- References -- Model-Based Inverse Regression and Its Applications -- 1 Introduction -- 1.1 Model-Based Inverse Reduction -- 1.2 Sufficient Reduction in Applications -- 2 Inverse Reduction for Multivariate Count Data -- 2.1 Multinomial Inverse Regression in Text Analysis -- 2.2 Predictive Learning in Metagenomics via Inverse Regression -- 2.3 Poisson Graphical Inverse Regression -- 3 Inverse Reduction and Its Dual -- 3.1 Reduction via Principal Coordinate Analysis -- 3.2 A Supervised Inverse Regression Model -- 4 Adaptive Independence Test via Inverse Regression -- 5 Cook's Contributions on Model-Based Sufficient Reduction -- References -- Sufficient Dimension Folding with Categorical Predictors -- 1 Introduction -- 2 Review on Sufficient Dimension Folding -- 3 Sufficient Dimension Folding with Categorical Predictors -- 4 Estimation Methods -- 4.1 Individual Direction Ensemble Method -- 4.2 Least Squares Folding Approach (LSFA) -- 4.3 Objective Function Optimization Method -- 5 Estimation of Structural Dimensions -- 6 Numerical Analysis -- 6.1 Simulation Studies -- 6.1.1 Part I (Continuous Y, Forward Model) -- 6.1.2 Part II (Discrete Y, Inverse Model) -- 6.2 Application -- 7 Discussion -- 8 Appendix -- 8.1 Proofs -- 8.2 Additional Simulation and Data Analysis -- Three Histograms for the Real Data -- The Bootstrap Confidence Interval Plots for Real Data -- References -- Sufficient Dimension Reduction Through Independenceand Conditional Mean Independence Measures -- 1 Introduction -- 2 Estimating SY|X Through ?-Distance Covariance -- 2.1 ?-Distance Covariance -- 2.2 Estimation of the Central Space. 327 $a3 Estimating SE(Y|X) Through ?-Martingale Difference Divergence -- 3.1 ?-Martingale Difference Divergence -- 3.2 Estimation of the Central Mean Space -- 4 Simulation Studies -- 4.1 Model Setup -- 4.2 Comparisons of Estimating the Central Space -- 4.3 Comparisons of Estimating the Central Mean Space -- 5 Analysis of the Iris Data -- 6 Conclusion -- Appendix -- References -- Cook's Fisher Lectureship Revisited for Semi-supervised DataReduction -- 1 Introduction -- 2 Dimension Reduction by Isotonic Models -- 2.1 Construction of Isotonic Model -- 2.2 Maximum Likelihood Estimation of ? -- 3 Numerical Examples -- 4 Real Data Example -- 5 Discussion -- References. 606 $aStatistics 606 $aMathematical statistics 606 $aEstadística matemàtica$2thub 608 $aHomenatges$2thub 608 $aLlibres electrònics$2thub 615 0$aStatistics. 615 0$aMathematical statistics 615 7$aEstadística matemàtica 676 $a519.5 702 $aBura$b Efstathia 702 $aLi$b Bing 702 $aCook$b R. 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