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This textbook provides a unified and self-contained presentation of the main approaches to and ideas of mathematical statistics. It collects the basic mathematical ideas and tools needed as a basis for more serious study or even independent research in statistics. The majority of existing textbooks in mathematical statistics follow the classical asymptotic framework. Yet, as modern statistics has changed rapidly in recent years, new methods and approaches have appeared. The emphasis is on finite sample behavior, large parameter dimensions, and model misspecifications. The present book...

The present book provides a fully self-contained introduction to the world of modern mathematical statistics, collecting the basic knowledge, concepts and findings needed for doing further research in the modern theoretical and applied statistics.

This volume provides an exposition of some fundamental aspects of the asymptotic theory of statistical experiments. The most important of them is "how to construct asymptotically optimal decisions if we know the structure of optimal decisions for the limit experiment".