Statistical Inference

Front Cover
Adopting a broad view of statistical inference, this text concentrates on what various techniques do, with mathematical proofs kept to a minimum. The approach is rigorous, but will be accessible to final year undergraduates. Classical approaches to point estimation, hypothesis testing andinterval estimation are all covered thoroughly, with recent developments outlined. Separate chapters are devoted to Bayesian inference, to decision theory and to non-parametric and robust inference. The increasingly important topics of computationally intensive methods and generalised linear modelsare also included. In this edition, the material on recent developments has been updated, and additional exercises are included in most chapters.
 

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Contents

Introduction
1
12 Plan of the book
3
13 Notation and terminology
4
Properties of estimators
7
23 Consistency
8
24 Efficiency
10
25 Sufficiency
18
26 Exponential families of distributions
27
66 Interval estimation
132
67 Bayesian sequential procedures
133
68 Exercises
144
Bayesian inference
151
73 Credible intervals
154
74 Hypothesis testing
158
75 Nuisance parameters
164
76 Noninformative stopping
168

27 Complete sufficient statistics
31
28 Problems with MVUEs
33
29 Summary
34
Maximum likelihood and other methods of estimation
40
33 Modifications and extensions of maximum likelihood estimation
54
34 Other methods of estimation
60
35 Discussion
63
36 Exercises
64
Hypothesis testing
71
43 Pure significance tests
77
44 Composite hypothesesuniformly most powerful tests
78
45 Further properties of tests of hypothesis
83
46 Maximum likelihood ratio tests
84
47 Alternatives to and modifications of maximum likelihood ratio tests
89
48 Discussion
92
49 Exercises
93
Interval estimation
97
52 Construction of confidence sets
98
53 Optimal properties of confidence sets
106
54 Some problems with confidence sets
108
55 Exercises
111
The decisiontheory approach to inference
114
62 Elements of decision theory
115
63 Point estimation
117
64 Loss functions and prior distributions
122
65 Hypothesis testing
128
77 Hierarchical models
170
78 Empirical Bayes
173
79 Exercises
178
Nonparametric and robust inference
185
82 Nonparametric hypothesis testing
186
83 Nonparametric estimation
199
84 Goodnessoffit tests and related techniques
201
85 Semiparametric methods
203
86 Robust inference
204
87 Exercises
212
Computationally intensive methods
217
93 Permutation and randomization tests
222
94 Crossvalidation
227
95 Jackknife and bootstrap methods
230
96 Gibbs sampling and related methodology
244
97 Exercises
256
Generalized linear models
265
102 Specifying the model
266
103 Fitting a generalized linear model using maximum likelihood
270
104 Deciding if the model fits the data
278
105 Model checking for glms
287
106 Quasilikelihood
295
107 Exercises
305
Bibliography
308
Index
319
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About the author (2002)

Paul Garthwaite is in the Department of Statistics, Open University, UK. Ian Jolliffe is a Professor of Statistics, University of Aberdeen. Byron Jones is a Director, Research Statistics Unit, GlaxoSmithKline, UK.

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