Symbolic computation for approximating distributions of some families of one and two-sample nonparametric test statistics

Authors:
Riccardo Gatto
Affiliations:
Institut für Mathematische Statistik und Versicherungslehre, Universität Bern, Switzerland. gatto@stat.unibe.cn
Venue:
Statistics and Computing
Year:
2001

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Abstract

A conditional saddlepoint approximation was provided by Gatto and Jammalamadaka (1999) for computing the distribution function of many test statistics based on dependent quantities like multinomial frequencies, spacing frequencies, etc. The considerable complexity of the formulas involved can be bypassed by symbolic computation. This article illustrates the effectiveness of symbolic computation to evaluate the saddlepoint approximation for the likelihood ratio, the exponential score, and the Wald-Wolfowitz test statistics. The case of composite hypotheses is also discussed.