Description
Book SynopsisIn this book, an integrated introduction to statistical inference is provided from a frequentist likelihood-based viewpoint. Classical results are presented together with recent developments, largely built upon ideas due to R.A. Fisher. The term “neo-Fisherian” highlights this.After a unified review of background material (statistical models, likelihood, data and model reduction, first-order asymptotics) and inference in the presence of nuisance parameters (including pseudo-likelihoods), a self-contained introduction is given to exponential families, exponential dispersion models, generalized linear models, and group families. Finally, basic results of higher-order asymptotics are introduced (index notation, asymptotic expansions for statistics and distributions, and major applications to likelihood inference).The emphasis is more on general concepts and methods than on regularity conditions. Many examples are given for specific statistical models. Each chapter is supplemented with problems and bibliographic notes. This volume can serve as a textbook in intermediate-level undergraduate and postgraduate courses in statistical inference.
Table of ContentsStatistical models; data and model reduction; survey of basic concepts and techniques; survey of basic concepts and techniques; pseudo-likelihoods; exponential families; exponential dispersion families; group families; asymptotic methods; asymptotic expansions for statistics; asymptotic expansions for distributions; likelihood and higher-order asymptotics. Appendices: convergence of suns; extreme value theory; basic terminology; frequency-decision and Fisherian paradigms.
