Expansions and Asymptotics for Statistics

The contents about Laplace approximation and saddlepoint approximation are pretty good and deep enough, while assuming little mathematical background of the readers. Some topics like summation of series are not usual ones contained in other books. I learned a lot when I took Prof. Small's course using this book as our textbook. However, if you are looking for a comprehensive book for asymptotic statistics, covering topics like M-estimator, von Mise statitical functional, bootstrap, I would suggest van der vaart's asymptotic statistics. For thorough treatment on likelihood method and related higher order theory, I recommend Barndoff-Nielson and Cox's Inference and asymptotics.

This book is based on the lecture notes on asymptotic method in statistics given at University of Waterloo. It is easy to follow and also provides rich historical backgrounds on the development of theory. It can be a handy reference especially when you want to refresh or sharpen your knowledge of asymptotic techniques.

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