Statistical Planning and Inference - Ghosh, Subir

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Résumé :

Preface xi

1 Foundation of Experiments 1

1.1 Uncertainties in Evidences 1

1.2 Examples 2

1.2.1 The Louis Pasteur Anthrax Vaccination Experiment 2

1.2.2 The Lanarkshire Milk Experiment: Milk Tests in Lanarkshire Schools 2

1.3 Replication, Randomization, Blocking, and Blinding 4

1.3.1 Replication 4

1.3.2 Randomization 4

1.3.3 Blocking 4

1.3.4 Blinding 4

1.4 Figuring It Out! 4

Questions and Answers 5

Bibliography 6

2 Completely Randomized Design 7

2.1 An Example 7

2.2 Analyses Using R and SAS 9

2.3 Figuring It Out! 12

Bibliography 16

3 Randomized Complete Block Design 17

3.1 Fixed Effects Model 18

3.2 Binomial Model for Signs 20

3.3 Randomization Model 20

3.4 Mixed Effects Model 25

3.5 General Mixed Effects Model 27

3.6 The REML Variance Components Estimates 28

3.7 BLUEs and BLUPs 31

3.7.1 The Conditional Model 32

3.7.2 The Unconditional Model 32

3.7.3 Computation-The Conditional Model 33

3.7.4 Computation-The Unconditional Model 34

3.8 Figuring It Out! 39

Bibliography 40

4 Randomized Incomplete Block Design 41

4.1 Model M1: Fixed-Effects Model 41

4.2 Model M2: Mixed-Effects Model 43

4.3 Research Questions 44

4.4 Figuring It Out! 45

4.5 Definitions 46

Exercises 46

Bibliography 51

5 Error Rates 53

5.1 Definitions of Error Rates 53

5.2 Single-Stage Methods 55

5.3 A Multistage Method 56

5.3.1 Benjamini and Hochberg Method 57

5.4 Figuring It Out 58

Questions 59

Bibliography 62

6 Nutrition Experiment 63

6.1 Figuring It Out! 63

Bibliography 75

7 The Pearson Dependence 77

7.1 Bivariate Normal Distribution 77

7.2 Estimation of Unknown Parameters 79

7.2.1 The Unconditional Model 79

7.2.2 The Conditional Model 81

7.2.3 Test of Significance 83

7.3 A Bayesian Estimation 84

7.4 Exercises 86

Bibliography 87

8 The Multivariate Dependence 89

8.1 The Multivariate Normal Distribution 90

8.2 Inference 91

8.3 Partial Dependence 96

8.4 Exercises 96

Bibliography 98

9 The Conditional Mean Dependence 99

9.1 LS Estimation 100

9.2 Ridge Estimation 101

9.2.1 A Bayesian Estimation 103

9.3 Dependence of Ridge Estimator on the Tuning Parameter 103

9.4 LASSO Estimation 104

9.5 Dependence of LASSO Estimators on the Tuning Parameter 105

Bibliography 116

10 More Parameters Than Observations 119

10.1 Learning by Doing-Exercises 122

Exercises 123

Bibliography 125

11 Eigenvalues, Eigenvectors, and Applications 127

11.1 Eigenvalues and Eigenvectors 127

11.2 Second-Order Response Surface 129

Exercises 132

Bibliography 133

12 Covariance Estimation 135

12.1 Model 1 135

12.1.1 Characterization of the Covariance Matrix and Its Estimators 135

12.1.2 Likelihood Function 136

12.1.3 Properties 137

12.2 Model 2 137

12.2.1 Characterization of the Covariance Matrix and Its Estimators 138

12.3 Model 3 138

12.4 Model 4 139

12.5 Model 5 140

12.6 Exercises 141

Bibliography 142

13 Discriminant Analysis 145

13.1 Learning from the Univariate Data-Two Normal Populations with Equal Variances 145

13.1.1 Discriminant Analysis for the Univariate Data 147

13.1.2 Example-Univariate Discriminant Analysis 148

13.2 Learn...

Biographie:

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.