Exact expected values of variance estimators for simulation

Abstract

Abstract:We formulate exact expressions for the expected values of selected estimators of the variance parameter (that is, the sum of covariances at all lags) of a steady-state simulation output process. Given in terms of the autocovariance function of the process, these expressions are derived for variance estimators based on the simulation analysis methods of nonoverlapping batch means, overlapping batch means, and standardized time series. Comparing estimator performance in a first-order autoregressive process and the M/M/1 queue-waiting-time process, we find that certain standardized time series estimators outperform their competitors as the sample size becomes large.

Revisit the Dynamic-Batch-Means Estimator

“…In addition, estimating the variance of the sample mean is also crucial in calculating confidence and prediction intervals of the population mean and the probability of selecting from alternatives correctly. Variance-estimation algorithms requiring (1) O memory storage without requiring the value of n a priori are needed when either the sample size is unknown a priori or the sample size is extremely large. The DNBM and DPBM estimators are the only two existing finite-memory algorithms for estimating the variance of the sample mean that do not require knowledge of the sample size a priori.…”

SPSTS: A sequential procedure for estimating the steady-state mean using standardized time series

“…Proof of Theorem 1 Parts of this proof run parallel to Theorem 3 and the corresponding examples in Aktaran-Kalaycı et al (2007). We use the notation f j (t) = f cos, j (t).…”

“…ofAktaran-Kalaycı et al (2007) and the references cited therein. The effect of j with respect to the magnitude of the negative bias of A ( f cos, j ; 1, m) is apparent.…”

A Finite-Memory Algorithm for Batch Means Estimators in Simulation Output Analysis

“…This research paper addresses the first issue; the second issue was studied in [13]. Song and Schmeiser [12] showed that nvar(Y n) = 0 2 0 1 2 n + o(n 01 ) (1) where 0 = 1 + 2 1 h=1 h is the sum of all correlations and 1 = 2 1 h=1 h h is the sum of all weighted correlations. The lag-h correlation of Y i and Y i+h , h = corr(Y i ; Y i+h ), satisfies h = O( h ) for h = 1; 2; .…”

“…The lag-h correlation of Y i and Y i+h , h = corr(Y i ; Y i+h ), satisfies h = O( h ) for h = 1; 2; . .., with 2 (0; 1) to reflect a general correlation structure for a wide range of stochastic processes, including waiting times in a steady-state M/M/1 queueing system [1].…”