Selection procedures with standardized time series variance estimators

Abstract

This article studies a modification of Rinott's two-stage procedure for selecting the normal population with the largest (or smallest) mean. The modification, which is appropriate for use in the simulation environment, uses in the procedure's first stage different variance estimators than the usual batch means (BM) variance estimator. In particular, we will use variance estimators arising from the method of standardized time series (STS). On the plus side, certain STS estimators have more degrees of freedom than that of the BM estimator. On the other hand, STS variance estimators tend to require larger sample sizes than the BM estimator in order to converge to their assumed distributions. These considerations result in trade-offs involving the procedure's achieved probability of correct selection as well as the procedure's expected sample size.

Ranking and Selection Techniques with Overlapping Variance Estimators for Simulations

“…The following two-stage "indifference-zone" procedure is an extension for use in steady-state simulation of Rinott's (1978) classic procedure, and was studied in Goldsman and Marshall (1999) and Goldsman et al (2002). For more details on Rinott's procedure, see Mukhopadhyay (1979).…”

On the Asymptotic Validity of Fully Sequential Selection Procedures for Steady-State Simulation

“…Goldsman et al (2002) present an extensive empirical evaluation based on a larger, but different, collection of examples, and our recommendations are also influenced by their results. As a baseline, we compare our procedures to procedure +, due to Goldsman and Marshall (1999), which modifies Rinott's (1978) procedure by replacing the usual sample variance of each system with an estimator of the asymptotic variance. Procedure + has two stages: In the first stage, an initial sample of size n 0 is taken from each system and used to estimate the asymptotic variance and compute the second-stage sample size.…”

“…These disadvantages have fostered efforts to develop new procedures designed specifically for steady-state simulation, procedures that can be applied to a single replication from each alternative and that use basic outputs rather than batch means. Goldsman and Marshall (1999) extended Rinott's (1978) procedure for use in steady-state simulation. Nakayama (1997) presented single-stage multiple-comparison procedures, and Damerdji and Nakayama (1999) developed two-stage multiplecomparison procedures, to provide inference on the best system for steady-state simulation.…”