The Symbolic Computation of Asymptotic Expansions,
TORONTO UNIV (ONTARIO)
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We describe a collection of procedures, coded in Mathematica, for the systematic computation of asymptotic expansions common in statistical theory and practice. The procedures permit the expansion of maximum likelihood estimates, the associated deviance or drop in likelihood, and more general functions of random variables involving one or an arbitrary number of parameters. General expansions, written in standard notation, are produced by these procedures and they can be evaluated for a particular distribution through the specification of the appropriate moment generating function. These procedures perform complex, lengthy derivations in a fraction of the time it takes by hand, with very little chance for error. They permit the statistician to concentrate on the structure of a symbolic calculation rather than on the detail of term by term evaluation. The procedures are illustrated with examples involving general laws.
- Statistics and Probability