In All Likelihood: Statistical Modelling and Inference Using Likelihood

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OUP Oxford, Jan 17, 2013 - Mathematics - 544 pages
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Based on a course in the theory of statistics this text concentrates on what can be achieved using the likelihood/Fisherian method of taking account of uncertainty when studying a statistical problem. It takes the concept ot the likelihood as providing the best methods for unifying the demands of statistical modelling and the theory of inference. Every likelihood concept is illustrated by realistic examples, which are not compromised by computational problems. Examples range from a simile comparison of two accident rates, to complex studies that require generalised linear or semiparametric modelling. The emphasis is that the likelihood is not simply a device to produce an estimate, but an important tool for modelling. The book generally takes an informal approach, where most important results are established using heuristic arguments and motivated with realistic examples. With the currently available computing power, examples are not contrived to allow a closed analytical solution, and the book can concentrate on the statistical aspects of the data modelling. In addition to classical likelihood theory, the book covers many modern topics such as generalized linear models and mixed models, non parametric smoothing, robustness, the EM algorithm and empirical likelihood.
 

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Contents

1 Introduction
1
2 Elements of likelihood inference
21
3 More properties of likelihood
53
4 Basic models and simple applications
73
5 Frequentist properties
117
regression models
149
7 Evidence and the likelihood principle
193
8 Score function and Fisher information
213
12 EM Algorithm
341
13 Robustness of likelihood specification
365
14 Estimating equations and quasilikelihood
385
15 Empirical likelihood
409
16 Likelihood of random parameters
425
17 Random and mixed effects models
435
18 Nonparametric smoothing
473
Bibliography
503

9 Largesample results
231
10 Dealing with nuisance parameters
273
11 Complex data structures
297

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About the author (2013)

Yudi Pawitan is a Professor in the Department of Medical Epidemiology and Biostatistics at the Karolinska Institutet in Sweden.

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