Abstract
Durbin (Biometrika 48:41–55, 1961) proposed a method called random substitution, by which a composite problem of goodness-of-fit can be reduced to a simple one. In this paper we provide a method of finding the p-value of any test statistic, for a composite goodness-of-fit problem, based on the simulation of a large number of conditional samples, using an analog of Durbin’s proposal in a reverse-type application. We analyze a Bayesian chi-square test proposed in Johnson (Ann Stat 32:2361–2384, 2004) which relies on a single randomization and relate it with Durbin’s original method. We also review a related proposal for conditional Monte-Carlo simulation in Lindqvist and Taraldsen (Biometrika 92:451–464, 2005) and compare it with our procedure. We show our method in a non-group example introduced in Lindqvist and Taraldsen (Biometrika 90:489–490, 2003).
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González-Barrios, J.M., O’Reilly, F. & Rueda, R. Durbin’s random substitution and conditional Monte Carlo. Metrika 72, 369–383 (2010). https://doi.org/10.1007/s00184-009-0258-z
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DOI: https://doi.org/10.1007/s00184-009-0258-z