Series Approximation Methods in Statistics

John E. Kolassa is Assistant Professor of Biostatistics at the University of Rochester.

• Asymptotics in General.- Characteristic Functions and the Berry-Esseen Theorem.- Edgeworth Series.- Saddlepoint Series for Densities.- Saddlepoint Series for Distribution Functions.- Multivariate Expansions.- Conditional Distribution Approximations.- Applications to Wald, Likelihood Ratio, and Maximum Likelihood Statistics.- Other Topics.- Computational Aids.

From the reviews of the third edition: "This book provides several important theoretical results that are relevant to Edgeworth and saddlepoint approximation to distribution functions, as well as to densities, in a simple and concise manner. ... The current edition showcases a rich and expanded list of references, exercises, and some applications. ... Two of the nice features of this book are its uniformity in notation and special attention to regularity conditions." (Technometrics, Vol. 49 (2), 2007) "This third edition features an expanded collection of references, exercises, and applications. Results have been reconfigured to adhere to a more conventional 'theorem/proof' format, which should make the material more tractable to some readers. Kolassa's updated text should continue to serve as a valuable resource for interested students and researchers on saddlepoint methods and Edgeworth expansions." (Joseph Cavanaugh, Journal of the American Statistical Association, Vol. 102 (480), 2007)