A BATCH MEANS METHODOLOGY FOR ESTIMATION OF A NONLINEAR FUNCTION OF ASTEADY-STATE MEAN

We study the estimation of steady-state performance measures from an R -d-valued stochastic process Y = {Y(t) : t greater than or equal to 0} representing the output of a simulation. In many applications, we may be interested in the estimation of a steady-state performance measure that cannot be expressed as a steady-state mean r, e.g., the variance of the steady-state distribution, the ratio of steady-state means, an d steady-state conditional expectations. These examples are particular cases of a more general problem-the estimation of a (nonlinear) funct ion f(r) of r. We propose a batch-means-based methodology that allows us to use jackknifing to reduce the bias of the point estimator. Asymp totically valid confidence intervals for f(r) are obtained by combinin g three different point estimators (classical, batch means, and jackkn ife) with two different variability estimators (classical and jackknif e). The performances of the point estimators are discussed by consider ing asymptotic expansions for their biases and mean squared errors. Ou r results show that, if the run length is large enough, the jackknife point estimator provides the smallest bias, with no significant increa se in the mean squared error.