Control variates for monte carlo analysis of nonlinear statistical models, II: raw moments and variances

Appoximations and Monte Carlo methods for evaluating the statistical properties of estimators for nonlinear—model parameters are discussed in Swain and Schmeiser (1984), where low—order polynomial approximators are used as control variates. Here, these control variates are specialized and applied to the raw marginal moments and the variance matrix of the parameter estimators. As an example, a catalytic—reaction model is studied empirically, with emphasis on the relationship between the control weights and variance reduction obtained. In this example, as well as in many others, the generalized variance of the estimator of the mean is reduced by orders of magnitude.