Control variates for monte carlo analysis of nonlinear statisticalmodels. IV

A Monte Carlo control variate method is used to study the estimators obtained in nonlinear regression under nonnormal error distributions. Two forms of the standard linear approximator are used as the control variates: a natural approximator using the nonnormal errors sampled, and a normalized approximator obtained by transformation of the errors. The natural approximator is shown to be most effective when the sampling distribution is itself nonnormal; its effectiveness is well approximated by a function of the Beale measure of nonlinearity. The normalized approximator is most effective when the estimator sampling distribution is approximately normal. A one-parameter model is used for illustration with uniform and gamma distributed errors