Expansions and Asymptotics for Statistics

Providing a broad toolkit of analytical methods, this book shows how asymptotics, when coupled with numerical methods, becomes a powerful way to acquire a deeper understanding of the techniques used in probability and statistics. It describes core ideas in statistical asymptotics; covers Laplace approximation, the saddle-point method, and summation of series; and includes vignettes of various people from statistics and mathematics whose ideas have been instrumental in the development...
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Providing a broad toolkit of analytical methods, this book shows how asymptotics, when coupled with numerical methods, becomes a powerful way to acquire a deeper understanding of the techniques used in probability and statistics. It describes core ideas in statistical asymptotics; covers Laplace approximation, the saddle-point method, and summation of series; and includes vignettes of various people from statistics and mathematics whose ideas have been instrumental in the development of the subject. The author also supplements some topics with relevant Maple commands and provides a list of common series and products, enabling readers to expand an expression or simplify an expansion.