Monte Carlo Analysis of Nonlinear Statistical Models. I. Theory. Revision.

Parameter values of nonlinear statistical models are typically estimated from data using iterative numerical procedures. The resulting joint sampling distribution of the parameter estimators is often intractable, resulting in the use of approximators or Monte Carlo simulation to determine properties of the sampling distribution. This paper develops methods, using linear and quadratic approximators as control variates, that reduce the variance of the Monte Carlo estimator by orders of magnitude. Estimation of means, higher order raw moments, variances, covariances, and percentiles is considered. (Author)