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Statistical Inference Based on the Likelihood


Author(s): Azzalini, A.
ISBN10:  041260650X
ISBN13:  9780412606502
Format:  Hardcover
Pub. Date:  6/1/1996
Publisher(s): Chapman & Hall/

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Table of Contents
Preface ix
1 Introduction and overview
1(16)
1.1 Statistical inference
1(3)
1.2 Sampling
4(1)
1.3 Statistics and probability
5(2)
1.4 Some typical problems
7(6)
1.5 Statistics and real problems
13(1)
Exercises
14(3)
2 Likelihood
17(34)
2.1 Statistical models
17(5)
2.2 Statistical likelihood
22(7)
2.3 Sufficient statistics
29(9)
2.4 Exponential families
38(9)
Exercises
47(4)
3 Maximum likelihood estimation
51(54)
3.1 Introduction
51(17)
3.2 Fisher information
68(10)
3.3 Properties of the MLE
78(14)
3.4 Some numerical examples
92(8)
Exercises
100(5)
4 Hypothesis testing
105(58)
4.1 General aspects
105(5)
4.2 Three test statistics related to the likelihood
110(6)
4.3 Likelihood ratio test
116(6)
4.4 Some important applications
122(19)
4.5 Interval estimation
141(18)
Exercises
159(4)
5 Linear models
163(60)
5.1 Relationships among variables
163(4)
5.2 Second-order hypotheses
167(18)
5.3 Normal theory
185(6)
5.4 Some important applications
191(21)
5.5 On model selection
212(6)
Exercises
218(5)
6 Generalized linear models
223(42)
6.1 Some limitations of linear models
223(3)
6.2 Generalized linear models
226(16)
6.3 Examining model adequacy
242(5)
6.4 Applications to frequency tables
247(11)
6.5 Quasi-likelihood
258(4)
Exercises
262(3)
Appendix: Complements of probability theory
265(48)
A.1 Inequalities
265(4)
A.2 Some univariate continuous distributions
269(6)
A.3 Some univariate discrete distributions
275(3)
A.4 Random vectors: general concepts
278(6)
A.5 The multivariate normal distribution
284(13)
A.6 The multinomial distribution
297(3)
A.7 Order statistics
300(3)
A.8 Sequences of random variables
303(7)
Exercises
310(3)
Main abbreviations and symbols 313(2)
Answers to selected exercises 315(8)
Essential bibliography 323(2)
References 325(4)
Author index 329(2)
Subject index 331

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