Festschrift in Honor of R. Dennis Cook : Fifty Years of Contribution to Statistical Science

In honor of professor and renowned statistician R. Dennis Cook, this festschrift explores his influential contributions to an array of statistical disciplines ranging from experimental design and population genetics, to statistical diagnostics and all areas of regression-related inference and analysis. Since the early 1990s, Prof. Cook has led the development of dimension reduction methodology in three distinct but related regression contexts: envelopes, sufficient dimension reduction (SDR), and regression graphics. In particular, he has made fundamental and pioneering contributions to SDR, inventing or co-inventing many popular dimension reduction methods, such as sliced average variance estimation, the minimum discrepancy approach, model-free variable selection, and sufficient dimension reduction subspaces. A prolific researcher and mentor, Prof. Cook is known for his ability to identify research problems in statistics that are both challenging and important, as well as his deep appreciation for the applied side of statistics. This collection of Prof. Cook's collaborators, colleagues, friends, and former students reflects the broad array of his contributions to the research and instructional arenas of statistics. 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 Proof 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 α-Distance Covariance 2.1 α-Distance Covariance 2.2 Estimation of the Central Space 3 Estimating SE(Y|X) Through α-Martingale Difference Divergence 3.1 α-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 Γ 3 Numerical Examples 4 Real Data Example 5 Discussion References