Theory of Statistics (Springer Series in Statistics)

Rating:
Summary: comprehensive, modern, rigorous treatment of stat theory
Review: This is the best book I've found that takes a modern approach to statistical theory at the advanced undergrad or graduate level. Schervish covers the necessary probability background, classical and Bayesian decision theory, and hypothesis testing comprehensively, while maintaining a level of rigor suitable for math majors (the appendix nicely summarizes requisite results from measure theory and mathematical probability). It covers most if not all of the classical results found in Lehmann's TSH and TPE, but from a more modern perspective. This permits a more coherent, well organized presentation. The only (minor) drawback I found were some typos here and there -- to be expected from a first edition of a 600 pager. It was a joy to study from this book.

Rating:
Summary: comprehensive, modern, rigorous treatment of stat theory
Review: This is the best book I've found that takes a modern approach to statistical theory at the advanced undergrad or graduate level. Schervish covers the necessary probability background, classical and Bayesian decision theory, and hypothesis testing comprehensively, while maintaining a level of rigor suitable for math majors (the appendix nicely summarizes requisite results from measure theory and mathematical probability). It covers most if not all of the classical results found in Lehmann's TSH and TPE, but from a more modern perspective. This permits a more coherent, well organized presentation. The only (minor) drawback I found were some typos here and there -- to be expected from a first edition of a 600 pager. It was a joy to study from this book.