Parametric statistical models and likelihood

Description

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.

Subjects

Series Statement

• Lecture notes in statistics ;