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.

Contents:

• Statistical Models
• Data and Model Reduction
• Survey of Some Basic Concepts and Techniques
• Nuisance Parameters and Pseudo-Likelihoods
• Exponential Families
• Exponential Dispersion Families and Generalized Linear Models
• Group Families
• Asymptotic Methods: Introduction and Elementary Techniques
• Asymptotic Expansions for Statistics
• Asymptotic Expansions for Distributions
• Likelihood and Higher-Order Asymptotics
• Laws of Large Numbers and Central Limit Theorems
• Asymptotic Distribution of Extremes
• Parametric Inference: Basic Terminology
• Relations Between the Frequency-Decision and Fisherian Paradigms

"An attractive feature of the book is that there are many examples to illustrate the theory ... the book is quite suitable as a reference or as supplementary reading material for an advanced graduate course ... this is a very useful book on statistical inference for graduate students and researchers."

"The pleasant feature of the book is that it contains a number of illustrative examples, each chapter is supplemented with problems to solve and with bibliograhic notes ... it is well written and can be really a useful book on principles of statistical inference for researchers as well as for PhD students."