Efficiency and exponential models in a variance-reduction technique for dichotomous response variables

Abstract

The statistical properties of a variance-reduction technique, applicable to simulations with dichotomous response variables, are examined from the standpoint of exponential models, that is, distribution families whose log-likelihood is a linear function of a sufficient statistic of fixed dimension. It is established that this variance-reduction technique induces some distortion that is explainable in terms of the statistical curvature of the resulting exponential model. The curvature concept used here is a multiparametric generalization of Efron's definition. It is calculated explicitly and its relation to the amount of variance reduction and to the asymptotic distribution of the relevant statistics is discussed. It is concluded that Efrons's criteria for low curvature (associated with nice statistical properties) are valid in this context and generally met for the usual sample sizes in simulation (some thousands of replicates).