Lehmann E.L., Romano J.P. Testing Statistical Hypotheses

4th ed. — Springer, 2022. — 1015 p. — (Springer Texts in Statistics). — ISBN 3030705773.The fourth edition of Testing Statistical Hypotheses provides a significant update to the third edition, which appeared in 2005. In order to accommodate new topics, one principal change from the third edition is the expansion of the book into two volumes. Volume I (Chapters 1–10) treats finite-sample theory, while Volume II (Chapters 11–18) treats asymptotic theory. A major addition to the treatment of finite-sample theory is a more expansive chapter (Chapter 9) on multiple hypothesis testing, including such topics as: the closure method, the false discovery rate, and other generalized error rates. A new section on the principle of monotonicity is included in Chapter 8. The asymptotic theory presented in Volume II has been reorganized. Chapter 12 covers asymptotic methods for sums of dependent variables and their application to inference. In particular, Chapter 12 includes: limit theorems for random sampling without replacement; some theory of U-statistics; central limit theorems for stationary, mixing processes; and Stein’s method. Chapter 13 includes an introduction to high-dimensional testing; see Section 13.5. The asymptotic theory of permutation and randomization tests is now expanded to its own chapter, Chapter 17, largely driven by the resurgence of such methodology. There are over 100 new problems in the volumes, bringing the total to around 900.True PDF