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Abstract:
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We propose a new resampling procedure, a variation of the Quasi-Bayesian bootstrap, for inference in the case of a single population proportion and for comparing two independent population proportions. As a semiparametric technique, the Quasi-Bayesian bootstrap offers an attractive alternative to the existing nonparametric and parametric bootstrap procedures. In our approach, we consider proportions as beta-distributed random variables, with parameter values determined using sample proportions and sample size. Variance estimates and confidence intervals are obtained in a two-stage Monte Carlo approach in which proportions are drawn from betas and samples (or sample proportions) then obtained given the drawn proportions. The idea is to account for sampling variability, and to reduce risk in the estimation of variances, particularly for small size samples (n?20). We present results of simulation studies showing that the Quasi-Bayesian variance estimators and confidence intervals outperform those of standard approaches based on mean square error (MSE) and confidence interval width, respectively. The method is applied to data from a cohort study of dental caries in children.
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