Symbolic Computation for Statistical Inference (Oxford Statistical Science Series, 21)

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Summary: a variety of statistical applications of symbol computation
Review: When I was a graduate student at Stanford I labored with tedious algebraic computations while trying to prove limit theorems for maxima of stationary sequences. Often it would be very frustrating as I would spend hours checking calculations only to repeatedly make minor mistakes that would cause results not to match. When properly programmed, this is ideal work for a computer. The computer can do the algebra flawlessly and much more quickly freeing the researcher to think about the harder problems. Mathematica was just coming out in the late 1970s but it was too late for my use. Now symbolic computing has advanced to the stage where we all should be using it. Andrews and Stafford make that point in this book. They cover many of the important mathematical results that are needed to solved advanced statistical problems. Edgeworth expansions, moment calculations and Taylor series expansions can all involve a great deal of tedious algebra. All these methods and their applications are exposed in this marvelous book. The authors also introduce us to an analytic bootstrap, Bartlett corrections, saddlepoint approximations, Cornish-Fisher expansions and Edgeworth expansions and applications to survey sampling designs. Chapter 3 goes into the fundamentals of symbolic computing and is the foundation needed for the applications that follow. This is a unique book that is valuable to any research statistician who may need to develop asymptotic results.