Combining standardized time series area and Cramér–von Mises variance estimators

Abstract

Abstract:We propose three related estimators for the variance parameter arising from a steady-state simulation process. All are based on combinations of standardized-time-series area and Cramér-von Mises (CvM) estimators. The first is a straightforward linear combination of the area and CvM estimators; the second resembles a Durbin-Watson statistic; and the third is related to a jackknifed version of the first. The main derivations yield analytical expressions for the bias and variance of the new estimators. These results show that the new estimators often perform better than the pure area, pure CvM, and benchmark nonoverlapping and overlapping batch means estimators, especially in terms of variance and mean squared error. We also give exact and Monte Carlo examples illustrating our findings.

An improved standardized time series Durbin–Watson variance estimator for steady-state simulation

“…and the result (13) follows by Equations (23) We know from [11] that for the MA(1), the following expectation holds exactly:…”

“…Now we will derive Var( D J,r (n)) for the MA (1) by calculating the components of Equation (27). First, we know from [11] that for the MA(1),…”

“…Among the estimators based on the STS methodology are the so-called area [14] and Cramér-von Mises (CvM) [12] estimators. Goldsman et al [11] combine these two types of estimators to obtain new STS estimators-the Durbin-Watson (DW) and jackknifed DW (JDW)-with competitive bias and lower asymptotic variance than many of their competitors. In this paper, we improve the JDW estimator in such a way that the resulting modified jackknifed DurbinWatson (MJDW) estimator has an asymptotic variance even smaller than that of the JDW estimator while maintaining almost the same bias value.…”

“…To reduce bias while maintaining small variance, a "jackknifed" (JDW) estimator is introduced in [11],…”

Ranking and Selection Techniques with Overlapping Variance Estimators for Simulations

“…It can be shown that the DW estimator has relatively low variance but suffers from high small-sample bias (Goldsman et al, 2007). To overcome this bias problem at only a modest cost in variance, Batur et al (2009) define the modified jackknifed DW estimator from the jth overlapping batch,…”