http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
Parametric Statistical Models and Likelihood
The book gives an account of the mathematical-statistical theory of the main classes of parametric statistical models, i.e. transformatioon models and exponential models, and of likelihood based inference. The emphasis is on recent developments - various new results are presented - and the mathematical techniques employed include parts of the theory of group actions and invariant measures, differential geometry, and asymptotic analysis. A knowledge of these techniques is not presupposed but will be helpful, as the exposition is partly quite succinct. A basic knowledge of classic parametric statistical inference is however assumed. Exactness results and high-order asymptotic results for important likelihood quantities, including maximum likelihood estimators, score vectors, (signed) likelihood ratios and (modified) profile likelihoods, are discussed. Concepts of ancillarity and sufficiency enter prominently.
Introduction -- Likelihood and auxiliary statistics -- Transformation models and exponential models -- Reparametrizations and differential geometry -- Inferential and geometric structures -- Cumulants -- Laplace's method, Edgeworth and saddle-point approximations -- Distributions of likelihood quantities -- Appendices -- References -- Subject Index.
Lecture notes in statistics (Springer-Verlag) ; 50