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