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Lourens Waldorp, Applied Asymptotics: Case Studies in Small Sample Statistics by Brazzale, A. R., Davison, A. C., and Reid, N., Biometrics, Volume 64, Issue 2, June 2008, Page 660, https://doi.org/10.1111/j.1541-0420.2008.01026_12.x
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This is an excellent book for applied statisticians. It presents applications of higher order asymptotic theory in likelihood in many different contexts. The book is generally well written and can be used by applied researchers to extend the presented case studies to include their own research interests.
Higher order asymptotic theory makes it possible to obtain very accurate distributional results in statistics. It is an important topic that has remained somewhat in the background in applied statistics and other sciences. The reason is, as the authors mention, that the theory can appear difficult and may not have a large impact in practice. This is unfortunate because many of the standard techniques for hypothesis testing can be greatly improved by using these results. The two co-authors, but especially Reid, are well known for their work in asymptotic theory. By writing this book, I think the authors have succeeded in making higher order theory more accessible and they will succeed in getting more scientists involved in this theory. The book can also be used as material for a course on higher order theory. There are sufficient problems of different levels of difficulty at the end of the book.
