Tools for the symbolic computation of asymptotic expansions

摘要: SUMMARY This paper describes a collection of procedures for the systematic computation asymptotic expansions that are common in statistical theory and practice: functions sums independent identically distributed random variables. The permit expansion maximum likelihood estimates, associated deviance or drop more general variables with distributions involving one parameters. illustrated examples specific laws. Much practice is based on expansions. Many programs available to assist numerical evaluation such expansions, but there need computational tools their derivation symbolic evaluation. Heller (1991) shows how calculation may be used wide variety problems. Kendall (1988, 1990) gives expressions analysis diffusion Euclidean shape. Silverman Young (1987) use computer algebra evaluate criteria which decision smooth bootstrap distribution based. Daniels (1990) apply assessment bias. Venables (1985) utilizes heavily obtain marginal most notably Fisher's A-statistic. Barndorff-Nielsen Blasild (1986) describe Bartlett factors cases where cumulants function specified. Most these references involve complicated formulae particular not themselves. Here we give both cases. typically simple laborious task. Consider, example, expectation ratio test statistic one-parameter family order 1/n. accomplished