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Statistical Models(2).pdf
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Contents
Preface
ix
1 Introduction
2 Variation
2.1 Statistics and Sampling Variation
2.2 Convergence
2.3 Order Statistics
2.4 Moments and Cumulants
2.5 Bibliographic Notes
2.6 Problems
3 Uncertainty
3.1 Confidence Intervals
3.2 Normal Model
3.3 Simulation
3.4 Bibliographic Notes
4 Likelihood
94
4.1 Likelihood
94
4.2 Summaries
101
4.3 Information
109
4.4 Maximum Likelihood Estimator
115
4.5 Likelihood Ratio Statistic
126
4.6 Non-Regular Models
140
v
vi
Contents
4.7 Model Selection
150
4.8 Bibliographic Notes
156
4.9 Problems
156
5 Models
161
5.1 Straight-Line Regression
161
5.2 Exponential Family Models
166
5.3 Group Transformation Models
183
5.4 Survival Data
188
5.5 Missing Data
203
5.6 Bibliographic Notes
218
5.7 Problems
219
6 Stochastic Models
225
6.1 Markov Chains
225
6.2 Markov Random Fields
244
6.3 Multivariate Normal Data
255
6.4 Time Series
266
6.5 Point Processes
274
6.6 Bibliographic Notes
292
6.7 Problems
293
7 Estimation and Hypothesis Testing
300
7.1 Estimation
300
7.2 Estimating Functions
315
7.3 Hypothesis Tests
325
7.4 Bibliographic Notes
348
7.5 Problems
349
8 Linear Regression Models
353
8.1 Introduction
353
8.2 Normal Linear Model
359
8.3 Normal Distribution Theory
370
8.4 Least Squares and Robustness
374
8.5 Analysis of Variance
378
8.6 Model Checking
386
8.7 Model Building
397
8.8 Bibliographic Notes
409
8.9 Problems
409
Contents
vii
9 Designed Experiments
417
9.1 Randomization
417
9.2 Some Standard Designs
426
9.3 Further Notions
439
9.4 Components of Variance
449
9.5 Bibliographic Notes
463
9.6 Problems
464
10 Nonlinear Regression Models
468
10.1 Introduction
468
10.2 Inference and Estimation
471
10.3 Generalized Linear Models
480
10.4 Proportion Data
487
10.5 Count Data
498
10.6 Overdispersion
511
10.7 Semiparametric Regression
518
10.8 Survival Data
540
10.9 Bibliographic Notes
554
10.10 Problems
555
11 Bayesian Models
565
11.1 Introduction
565
11.2 Inference
578
11.3 Bayesian Computation
596
11.4 Bayesian Hierarchical Models
619
11.5 Empirical Bayes Inference
627
11.6 Bibliographic Notes
637
11.7 Problems
639
12 Conditional and Marginal Inference
645
12.1 Ancillary Statistics
646
12.2 Marginal Likelihood
656
12.3 Conditional Inference
665
12.4 Modified Profile Likelihood
680
12.5 Bibliographic Notes
691
12.6 Problems
692
viii
Contents
Appendix A. Practicals
696
Bibliography
699
Name Index
712
Example Index
716
Index


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