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Biometrika 1997 84(1):235-240; doi:10.1093/biomet/84.1.235
© 1997 by Biometrika Trust
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MISCELLANEA

Stochastic simulations conditioned on sufficient statistics

STEINAR ENGEN and MAGNAR LILLEGÅRD

Department of Mathematics and Statistics, Norwegian University of Science and Technology N-7055 Dragvoll, Norway e-mail: steinar.engen{at}math.ntnu.no magnar.lillegard{at}math.ntnu.no

A general method for doing Monte Carlo simulations conditioned on sufficient statistics is presented. The basic idea is to adjust the parameter values in the corresponding unconditional simulation so that the actual value of the sufficient statistic is obtained. In the case of multiple solutions to this problem, the method has to be modiiied, even if the corresponding value of the simulated variable is unique for each simulation. The methods are illustrated for some simple models in which the conditional distributions are well known. As a more complicated example, an exact ‘analysis of variance’ test in the gamma model is performed. Other examples are a modifimtion of the Kolmogorov goodness-of-fit test into an exact test, and minimum variance unbiased estimation of cumulative distributions.

Key Words: Conditional distribution • Nuisance parameter • Stochastic simulation • Sufficient statistic


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