Likelihood Methods in Statistics (Oxford Statistical Science Series, 22)

This Book Provides An Introduction To The Modern Theory Of Likelihood-based Statistical Inference. This Theory Is Characterized By Several Important Features. One Is The Recognition That It Is Desirable To Condition On Relevant Ancillary Statistics. Another Is That Probability Approximations Are Based On Saddlepoint And Closely Related Approximations That Generally Have Very High Accuracy. A Third Aspect Is That, For Models With Nuisance Parameters, Inference Is Often Based On Marginal Or Conditional Likelihoods, Or Approximations To These Likelihoods. These Methods Have Been Shown To Often Yield Substantial Improvements Over Classical Methods. The Book Also Provides An Up-to-date Account Of Recent Results In The Field, Which Has Been Undergoing Rapid Development.--jacket. Some Basic Concepts -- Exponential Family Models -- Transformation Models -- Cumulants -- Sufficiency -- Ancillary Statistics -- Normal Distribution Theory -- Large-sample Approximations -- Central Limit Theorem -- Edgeworth Series Approximations -- Saddlepoint Approximation Of Densities -- Approximation Of Integrals And Sums -- Saddlepoint Approximations For Distribution Functions -- Saddlepoint Approximations For Lattice Variables -- Saddlepoint Approximations For Multivariate Distributions -- Stochastic Asymptotic Expansions -- Approximation Of Conditional Distributions -- Laplace Approximations -- Likelihood -- Some Properties Of The Likelihood Function -- The Likelihood Principle -- Regular Models -- Log-likelihood Derivatives -- Information -- Methods Of Inference -- First-order Asymptotic Theory -- Maximum Likelihood Estimates -- The Likelihood Ratio Statistic -- The Score And Wald Statistics -- Confidence Regions -- The Profile Likelihood Function -- Nonregular Models -- Higher-order Asymptotic Theory -- Some Preliminary Results -- Maximum Likelihood Estimates -- Likelihood Ratio Statistic -- Saddlepoint Approximations -- Asymptotic Theory And Conditional Inference -- Log-likelihood Derivatives -- Conditional Distribution Of Maximum Likelihood Estimates -- Stable Inference -- Approximation Of The Conditional Model -- Approximate Ancillarity -- Approximation Of Sample Space Derivatives -- The Signed Likelihood Ratio Statistic -- Normalizing Transformations -- One-parameter Models. Thomas A. Severini. Includes Bibliographical References (p. [362]-373) And Indexes.