统计推断原理 英文版PDF电子书下载

Example 1.1 The normal mean 3

Example 1.2 Linear regression 4

Example 1.3 Linear regression in semiparametric form 4

Example 1.4 Linear model 4

Example 1.5 Normal theory nonlinear regression 4

Example 1.6 Exponential distribution 5

Example 1.7 Comparison of binomial probabilities 5

Example 1.8 Location and related problems 5

Example 1.9 A component of variance model 11

Example 1.10 Markov models 12

Example 2.1 Exponential distribution(ctd) 19

Example 2.2 Linear model(ctd) 19

Example 2.3 Uniform distribution 20

Example 2.4 Binary fission 20

Example 2.5 Binomial distribution 21

Example 2.6 Fisher's hyperbola 22

Example 2.7 Binary fission(ctd) 23

Example 2.8 Binomial distribution(ctd) 23

Example 2.9 Mean of a multivariate normal distribution 27

Example 3.1 Test of a Poissonmean 32

Example 3.2 Adequacy of Poisson model 33

Example 3.3 More on the Poisson distribution 34

Example 3.4 Test of symmetry 38

Example 3.5 Nonparametric two-sample test 39

Example 3.6 Ratio of normal means 40

Example 3.7 Poisson-distributed signal with additive noise 41

Example 4.1 Uniform distribution of known range 47

Example 4.2 Two measuring instruments 48

Example 4.3 Linear model 49

Example 4.4 Two-by-two contingency table 51

Example 4.5 Mantel-Haenszel procedure 54

Example 4.6 Simple regression for binary data 55

Example 4.7 Normal mean,variance unknown 56

Example 4.8 Comparison of gamma distributions 56

Example 4.9 Unacceptable conditioning 56

Example 4.10 Location model 57

Example 4.11 Normal mean,variance unknown(ctd) 59

Example 4.12 Normal variance 59

Example 4.13 Normal mean,variance unknown(ctd) 60

Example 4.14 Components of variance 61

Example 5.1 Exchange paradox 67

Example 5.2 Two measuring instruments(ctd) 68

Example 5.3 Rainy days in Gothenburg 70

Example 5.4 The normal mean(ctd) 71

Example 5.5 The noncentral chi-squared distribution 74

Example 5.6 A set of binomial probabilities 74

Example 5.7 Exponential regression 75

Example 5.8 Components of variance(ctd) 80

Example 5.9 Bias assessment 82

Example 5.10 Selective reporting 86

Example 5.11 Precision-based choice of sample size 89

Example 5.12 Sampling the Poisson process 90

Example 5.13 Multivariate normal distributions 92

Example 6.1 Location model(ctd) 98

Example 6.2 Exponential family 98

Example 6.3 Transformation to near location form 99

Example 6.4 Mixed parameterization of the exponential family 112

Example 6.5 Proportional hazards Weibull model 113

Example 6.6 A right-censored normal distribution 118

Example 6.7 Random walk with an absorbing barrier 119

Example 6.8 Curved exponential family model 121

Example 6.9 Covariance selection model 123

Example 6.10 Poisson-distributed signal with estimated background 124

Example 7.1 An unbounded likelihood 134

Example 7.2 Uniform distribution 135

Example 7.3 Densities with power-law contact 136

Example 7.4 Model of hidden periodicity 138

Example 7.5 A special nonlinear regression 139

Example 7.6 Informative nonresponse 140

Example 7.7 Integer normal mean 143

Example 7.8 Mixture of two normal distributions 144

Example 7.9 Normal-theory linear model with many parameters 145

Example 7.10 A non-normal illustration 146

Example 7.11 Parametric model for right-censored failure data 149

Example 7.12 A fairly general stochastic process 151

Example 7.13 Semiparametric model for censored failure data 151

Example 7.14 Lag one correlation of a stationary Gaussian time series 153

Example 7.15 A long binary sequence 153

Example 7.16 Case-control study 154

Example 8.1 A new observation from a normal distribution 162

Example 8.2 Exponential family 165

Example 8.3 Correlation between different estimates 165

Example 8.4 The sign test 166

Example 8.5 Unbiased estimate of standard deviation 167

Example 8.6 Summarization of binary risk comparisons 171

Example 8.7 Brownian motion 174

Example 9.1 Two-by-two contingency table 190

1 Preliminaries 1

Summary 1

1.1 Starting point 1

1.2 Role of formal theory of inference 3

1.3 Some simple models 3

1.4 Formulation of objectives 7

1.5 Two broad approaches to statistical inference 7

1.6 Some further discussion 10

1.7 Parameters 13

Notes 1 14

2 Some concepts and simple applications 17

Summary 17

2.1 Likelihood 17

2.2 Sufficiency 18

2.3 Exponential family 20

2.4 Choice of priors for exponential family problems 23

2.5 Simple frequentist discussion 24

2.6 Pivots 25

Notes 2 27

3 Significance tests 30

Summary 30

3.1 General remarks 30

3.2 Simple significance test 31

3.3 One-and two-sided tests 35

3.4 Reladon with acceptance and rejection 36

3.5 Formulation of alternatives and test statistics 36

3.6 Relation with interval estimation 40

3.7 Interpretation of significance tests 41

3.8 Bayesian testing 42

Notes 3 43

4 More complicated situations 45

Summary 45

4.1 General remarks 45

4.2 General Bayesian formulation 45

4.3 Frequentist analysis 47

4.4 Some more general frequentist developments 50

4.5 Some further Bayesian examples 59

Notes4 62

5 Interpretations of uncertainty 64

Summary 64

5.1 General remarks 64

5.2 Broad roles of probability 65

5.3 Frequentist interpretation of upper limits 66

5.4 Neyman-Pearson operational criteria 68

5.5 Some general aspects of the frequentist approach 68

5.6 Yet more on the frequentist approach 69

5.7 Personalistic probability 71

5.8 Impersonal degree of belief 73

5.9 Reference priors 76

5.10 Temporal coherency 78

5.11 Degree of belief and frequency 79

5.12 Statistical implementation of Bayesian analysis 79

5.13 Model uncertainty 84

5.14 Consistency of data and prior 85

5.15 Relevance of frequentist assessment 85

5.16 Sequential stopping 88

5.17 A simple classification problem 91

Notes 5 93

6 Asymptotic theory 96

Summary 96

6.1 General remarks 96

6.2 Scalar parameter 97

6.3 Multidimensional parameter 107

6.4 Nuisance parameters 109

6.5 Tests and model reduction 114

6.6 Comparative discussion 117

6.7 Profile likelihood as an information summarizer 119

6.8 Constrained estimation 120

6.9 Semi-asymptotic arguments 124

6.10 Numerical-analytic aspects 125

6.11 Higher-order asymptotics 128

Notes 6 130

7 Further aspects of maximum likelihood 133

Summary 133

7.1 Multimodal likelihoods 133

7.2 Irregular form 135

7.3 Singular information matrix 139

7.4 Failure of model 141

7.5 Unusual parameter space 142

7.6 Modified likelihoods 144

Notes 7 159

8 Additional objectives 161

Summary 161

8.1 Prediction 161

8.2 Decision analysis 162

8.3 Point estimation 163

8.4 Non-likelihood-based methods 169

Notes 8 175

9 Randomization-based analysis 178

Summary 178

9.1 General remarks 178

9.2 Sampling a finite population 179

9.3 Design of experiments 184

Notes 9 192

Appendix A：A brief history 194

Appendix B：Apersonal view 197

References 201

Author index 209

Subject index 213