Use of the Gibbs Sampler to Obtain Conditional Tests, with Applications

A random sample is drawn from a distribution which admits aminimal sufficient statistic for the parameters. The Gibbs sampleris proposed to generate samples, called conditionally sufficientor co-sufficient samples, from the conditional distributionof the sample given its value of the sufficient statistic. Theprocedure is illustrated for the gamma distribution. Co-sufficientsamples may be used to give exact tests of fit; for the gammadistribution these are compared for size and power with approximatetests based on the parametric bootstrap.     

Diagnostic measures for empirical likelihood of general estimating equations

We develop diagnostic measures for assessing the influence ofindividual observations when using empirical likelihood withgeneral estimating equations, and we use these measures to constructgoodness-of-fit statistics for testing possible misspecificationin the estimating equations. Our diagnostics include case-deletionmeasures, local influence measures and pseudo-residuals. Ourgoodness-of-fit statistics include the sum of local influencemeasures and the processes of pseudo-residuals. Simulation studiesare conducted to evaluate our methods, and real datasets areanalyzed to illustrate the use of our diagnostic measures andgoodness-of-fit statistics.