Series Approximation Methods in Statistics (Lecture Notes in Statistics (88))

This revised book presents theoretical results relevant to Edgeworth and saddlepoint expansions to densities and distribution functions. It provides examples of their application in some simple and a few complicated settings, along with numerical, as well as asymptotic, assessments of their accuracy. Variants on these expansions, including much of modern likelihood theory, are discussed and applications to lattice distributions are extensively treated. This book was originally compiled for a course I taught at the University of Rochester in the fall of 1991, and is intended to give advanced graduate students in statistics an introduction to Edgeworth and saddlepoint approximations, and related techniques. Many other authors have also written monographs on this s- ject, and so this work is narrowly focused on two areas not recently discussed in theoretical text books. These areas are,?rst, a rigorous consideration of Edgeworth and saddlepoint expansion limit theorems, and second, a survey of the more recent developments in the?eld. In presenting expansion limit theorems I have drawn heavily on notation of McCullagh (1987) and on the theorems presented by Feller (1971) on Edgeworth expansions. For saddlepoint notation and results I relied most heavily on the many papers of Daniels, and a review paper by Reid (1988). Throughout this book I have tried to maintain consistent notation and to present theorems in such a way as to make a few theoretical results useful in as many contexts as possible. This was not only in order to present as many results with as few proofs as possible, but more importantly to show the interconnections between the various facets of asymptotic theory. Special attention is paid to regularity conditions. The reasons they are needed and the parts they play in the proofs are both highlighted. "Asymptotic techniques have long been important in statistical inference; these techniques remain important in the age of fast computing because some exact answers are still either conceptually unavailable or practically out of reach. This book presents theoretical results relevant to Edgeworth and saddlepoint expansions to densities and distribution functions." "This book is intended primarily for advanced graduate students and researchers in the field needing a collection of core results in a uniform notation, with bibliographical references to further examples and applications. It assumes familiarity with real and univariate complex analysis, and vector calculus."--Jacket

asymptotic Techniques Have Long Been Important In Statistical Inference; These Techniques Remain Important In The Age Of Fast Computing Because Some Exact Answers Are Still Either Conceptually Unavailable Or Practically Out Of Reach. This Book Presents Theoretical Results Relevant To Edgeworth And Saddlepoint Expansions To Densities And Distribution Functions. It Provides Examples Of Their Application In Some Simple, And In A Few Complicated, Settings. Numerical And Asymptotic Assessments Of Accuracy Are Presented. Variants Of These Expansions, Including Much Of Modern Likelihood Theory, Are Discussed. Applications To Lattice Distributions Are Extensively Treated.

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