ON THE CONVERGENCE-RATES OF IPA AND FDC DERIVATIVE ESTIMATORS

We show that under the (sufficient) conditions usually given for infin itesimal perturbation analysis (IPA) to apply for derivative estimatio n, a finite-difference scheme with common random numbers (FDC) has the same order of convergence, namely 0(n-1/2) , provided that the size o f the finite-difference interval converges to zero fast enough. This h olds for both one- and two-sided FDC. This also holds for different va riants of IPA, such as some versions of smoothed perturbation analysis (SPA), which is based on conditional expectation. Finally, this also holds for the estimation of steady-state performance measures by trunc ated-horizon estimators, under some ergodicity assumptions. Our develo pments do not involve monotonicity, but are based on continuity and sm oothness. We give examples and numerical illustrations which show that the actual difference in mean square error (MSE) between IPA and FDC is typically negligible. We also obtain the order of convergence of th at difference, which is faster than the convergence of the MSE to zero .