Principles of Statistical Inference from a Neo-Fisherian Perspective

In this book, an integrated introduction to the 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. After a unified review of background material (statistical methods, likelihood, data reductions, first-order asymptotics) and inference in the presence of nuisance parameters (including pseufo-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 exercises, problems and bibliographic notes. This volume can serve as a textbook in intermediate-level undergraduate courses.