Parametric Statistical Inference

Front Cover
Clarendon Press, 1996 - Mathematics - 490 pages
Inference involves drawing conclusions about some general phenomenon from limited empirical observations in the face of random variability. In a scientific context, the general must include the completely unforeseen if all possibilities are to be considered. Many of the statistical models most used to describe such phenomena belong to one of a small number of families--the exponential, transformation, and stable families. In the past 25 years, the likelihood function has been recognized as the fundamental element of approach to drawing scientific conclusions. This book brings together for the first time these two components of statistics as the central themes of statistical inference. Chapters focus on model building, approximations, and examples. There are also appendices on the elements of measure theory, probability theory, and numerical methods. The discussions are appropriate for students of mathematical statistics.
 

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Contents

Model building
7
Exponential family of probability distributions
25
Likelihood
69
Goodness of fit
141
Asymptotics
185
Factoring the likelihood function
233
Frequentist decisionmaking
279
Bayesian decisionmaking
321
Poisson regression
367
Binomial regression
385
A Elements of measure theory
407
Normal distribution statistics
435
Numerical methods
441
Index
469
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About the author (1996)

J. K. Lindsey is at University of Liege.

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