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

Abstract

We discuss an improved jackknifed Durbin-Watson estimator for the variance parameter from a steady-state simulation. The estimator is based on a combination of standardized time series area and Cramér-von Mises estimators. Various examples demonstrate its efficiency in terms of bias and variance compared to other estimators.

Boundary Crossing Probabilities for the Cumulative Sample Mean

“…Many researchers have used standardized time series methods to estimate the mean and variance of data that have some degree of serial dependency (Batur, Goldsman, and Kim [4], Goldsman, Meketon, and Schruben [9]). We take a different approach and exploit the properties of Brownian bridges to derive the probability the cumulative mean stays within some distance from the long-term mean and the true mean.…”

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,…”

Exact expected values of variance estimators for simulation

“…For other approaches to steady-state simulation output analysis, see, e.g., [13]. Ifσ 2 is a candidate estimator of σ 2 , then we may evaluate the performance ofσ 2 2 ]. Usually, the lower the bias and variance, the better.…”

“…If c 1,1 = c 2,1 = 0 (so that bothσ 2 1 andσ 2 2 are first-order unbiased for σ 2 ), then knowledge of the relative magnitudes of c 1,2 and c 2,2 would be helpful in determining which estimator has lower (second-order) bias. On the other hand, if c 1,1 = 0 but c 2,1 = 0 (so that onlyσ 2 1 is first-order unbiased), then it may still be the case that the constant c 1,2 is so prohibitively large thatσ 2 1 performs poorly in comparison withσ 2 2 for small batch sizes. In this case, it would be useful to determine which sample sizes guarantee Bias[σ 2 1 ] < Bias[σ 2 2 ].…”

“…On the other hand, if c 1,1 = 0 but c 2,1 = 0 (so that onlyσ 2 1 is first-order unbiased), then it may still be the case that the constant c 1,2 is so prohibitively large thatσ 2 1 performs poorly in comparison withσ 2 2 for small batch sizes. In this case, it would be useful to determine which sample sizes guarantee Bias[σ 2 1 ] < Bias[σ 2 2 ]. A second justification for our efforts is that the exact bias expressions can be used as follows: in seeking to minimize MSE[σ 2 ] as it depends on the batch size m = m(n) and the batch-size-to-sample-size ratio b = b(n) for large n, we obtain a smaller asymptotically optimal expression for MSE[σ 2 ] whenσ 2 has a higher-order unbiasedness property.…”