Statistical Planning and Inference

Subir Ghosh is a Professor of Statistics at the University of California, Riverside, USA. He is known for his research work in Statistical Design and Analysis of Experiments and Modeling. He is an elected fellow of the American Statistical Association, the American Association of the Advancement of Science, and an elected member of the International Statistical Institute. He received the awards at the University of California, Riverside:2012-2016 Distinguished Teaching Professor and a member of the UCR Academy of Distinguished Teachers.2003 Graduate Council Dissertation Advisor/Mentoring Award, and 1993 Academic Senate Distinguished Teaching Award.He also served as the 2000-2003 executive editor of the Journal of Statistical Planning and Inference.

• Preface xi1 Foundation of Experiments 11.1 Uncertainties in Evidences 11.2 Examples 21.2.1 The Louis Pasteur Anthrax Vaccination Experiment 21.2.2 The Lanarkshire Milk Experiment: Milk Tests in Lanarkshire Schools 21.3 Replication, Randomization, Blocking, and Blinding 41.3.1 Replication 41.3.2 Randomization 41.3.3 Blocking 41.3.4 Blinding 41.4 Figuring It Out! 4Questions and Answers 5Bibliography 62 Completely Randomized Design 72.1 An Example 72.2 Analyses Using R and SAS 92.3 Figuring It Out! 12Bibliography 163 Randomized Complete Block Design 173.1 Fixed Effects Model 183.2 Binomial Model for Signs 203.3 Randomization Model 203.4 Mixed Effects Model 253.5 General Mixed Effects Model 273.6 The REML Variance Components Estimates 283.7 BLUEs and BLUPs 313.7.1 The Conditional Model 323.7.2 The Unconditional Model 323.7.3 Computation—The Conditional Model 333.7.4 Computation—The Unconditional Model 343.8 Figuring It Out! 39Bibliography 404 Randomized Incomplete Block Design 414.1 Model M1: Fixed-Effects Model 414.2 Model M2: Mixed-Effects Model 434.3 Research Questions 444.4 Figuring It Out! 454.5 Definitions 46Exercises 46Bibliography 515 Error Rates 535.1 Definitions of Error Rates 535.2 Single-Stage Methods 555.3 A Multistage Method 565.3.1 Benjamini and Hochberg Method 575.4 Figuring It Out 58Questions 59Bibliography 626 Nutrition Experiment 636.1 Figuring It Out! 63Bibliography 757 The Pearson Dependence 777.1 Bivariate Normal Distribution 777.2 Estimation of Unknown Parameters 797.2.1 The Unconditional Model 797.2.2 The Conditional Model 817.2.3 Test of Significance 837.3 A Bayesian Estimation 847.4 Exercises 86Bibliography 878 The Multivariate Dependence 898.1 The Multivariate Normal Distribution 908.2 Inference 918.3 Partial Dependence 968.4 Exercises 96Bibliography 989 The Conditional Mean Dependence 999.1 LS Estimation 1009.2 Ridge Estimation 1019.2.1 A Bayesian Estimation 1039.3 Dependence of Ridge Estimator on the Tuning Parameter 1039.4 LASSO Estimation 1049.5 Dependence of LASSO Estimators on the Tuning Parameter 105Bibliography 11610 More Parameters Than Observations 11910.1 Learning by Doing—Exercises 122Exercises 123Bibliography 12511 Eigenvalues, Eigenvectors, and Applications 12711.1 Eigenvalues and Eigenvectors 12711.2 Second-Order Response Surface 129Exercises 132Bibliography 13312 Covariance Estimation 13512.1 Model 1 13512.1.1 Characterization of the Covariance Matrix and Its Estimators 13512.1.2 Likelihood Function 13612.1.3 Properties 13712.2 Model 2 13712.2.1 Characterization of the Covariance Matrix and Its Estimators 13812.3 Model 3 13812.4 Model 4 13912.5 Model 5 14012.6 Exercises 141Bibliography 14213 Discriminant Analysis 14513.1 Learning from the Univariate Data—Two Normal Populations with Equal Variances 14513.1.1 Discriminant Analysis for the Univariate Data 14713.1.2 Example—Univariate Discriminant Analysis 14813.2 Learning from the Univariate Data—Two Normal Populations with Unequal Variances 15113.2.1 Classification of 25 Versicolor Iris Flowers 15313.2.2 Classification of 25 Setosa Iris Flowers 15413.2.3 Test of Homogeneity of Variances 15413.3 Learning from the Multivariate Data 15513.3.1 Classification of Versicolor and Setosa 15613.3.2 Classification of Versicolor and Virginica 15813.4 Logistic Regression 15913.5 Exercises 160Bibliography 16214 Optimizing the Variance–Bias Trade-Off 16314.1 Variance–Bias Trade-Off 16314.1.1 Example 1 16414.1.2 Example 2 16514.1.3 Example 3 16614.2 Information in Data 16714.3 Information and Design in Presence of a Covariate 16914.3.1 Information 16914.3.2 Optimum Design for a Covariate 17014.4 Information and Design in Presence of Multiple Covariates 17114.4.1 Information 17114.4.2 Exponential Model 17514.4.3 Exponential Regression Model with Multiple Covariates 17614.4.4 Poisson Log-Linear Model 17714.4.5 Non-parametric Regression Model 18014.5 Exercises 183Bibliography 18715 Specification, Discrimination, Robustness, and Sensitivity 18915.1 The Global and Local Optimal Models 18915.2 The T-Optimal Design 19015.3 Convex and Concave Functions 19215.4 The Kullback–Leibler (KL) Divergence 19415.5 The KL Design Optimality 19715.6 The Differential Entropy 19815.7 Lindley Information Measure 20015.8 Joint Entropy, Conditional Entropy, and Mutual Information 20215.9 Maximum Entropy Sampling 20415.10 Search Linear Models and Search Designs 20715.10.1 Factorial Experiments 20915.10.2 Search Probability Matrix 21015.11 Robustness Against Unavailable Data 21015.12 Influential Sets of Observations 21215.13 Exercises 213Bibliography 214Data Index 217Subject Index 219