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Inference and Asymptotics (Hardcover)
Loot Price: R5,152
Discovery Miles 51 520
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Inference and Asymptotics (Hardcover)
Series: Chapman & Hall/CRC Monographs on Statistics and Applied Probability
Expected to ship within 12 - 17 working days
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Total price: R5,172
Discovery Miles: 51 720
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Likelihood and its many associated concepts are of central
importance in statistical theory and applications. The theory of
likelihood and of likelihood-like objects (pseudo-likelihoods) has
undergone extensive and important developments over the past 10 to
15 years, in particular as regards higher order asymptotics. This
book provides an account of this field, which is still vigorously
expanding. Conditioning and ancillarity underlie the p*-formula, a
key formula for the conditional density of the maximum likelihood
estimator, given an ancillary statistic. Various types of
pseudo-likelihood are discussed, including profile and partial
likelihoods. Special emphasis is given to modified profile
likelihood and modified directed likelihood, and their intimate
connection with the p*-formula. Among the other concepts and tools
employed are sufficiency, parameter orthogonality, invariance,
stochastic expansions and saddlepoint approximations. Brief reviews
are given of the most important properties of exponential and
transformation models and these types of model are used as
test-beds for the general asymptotic theory. A final chapter
briefly discusses a number of more general issues, including
prediction and randomization theory. The emphasis is on ideas and
methods, and detailed mathematical developments are largely
omitted. There are numerous notes and exercises, many indicating
substantial further results.
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