Cramer-von Mises variance estimators for simulations

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.

Section: Exact Results: Moving Average Processmentioning

confidence: 99%

“…Here, we define the notation G ≡ 1 0 g(t) dt. THEOREM 2 (see [13]): Under the conditions of Theorem 1,…”

Section: The Weighted Cramér-von Mises Estimatormentioning

confidence: 99%

Section: The Weighted Cramér-von Mises Estimatormentioning

confidence: 99%

See 1 more Smart Citation

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

Goldsman¹,

Kang²,

Kim³

et al. 2007

“…REMARK 1: A number of other estimators for u2 arise from standardized time series (see, e.g., [9]), spectral analysis [12], times series modeling [ 5 , 6, 171, regeneration theory [4], and overlapping batch means methods [15]. The limiting distributions of these estimators are sometimes tractable but not necessarily x2; for this reason, we will not use these estimators subsequently.…”

Section: Some Variance Estimatorsmentioning

confidence: 99%

“…b ' u2, which is unknown. If we are willing to estimate (or make a rough guess of) p 2 / u 2 , the combination of b , b', and k can be found that maximizes (9).…”

Section: Analytical Comparison Of Testsmentioning

confidence: 99%

Tests for transient means in simulated time series

Goldsman

Schruben

Swain

1994

We present a family of tests to detect the presence of a transient mean in a simulation process. These tests compare variance estimators from different parts of a simulation run, and are based on the methods of batch means and standardized time series. Our tests can be viewed as natural generalizations of some previously published work. We also include a power analysis of the new tests, as well as some illustrative examples. © 1994 John Wiley & Sons, Inc.

Exact expected values of variance estimators for simulation

Aktaran-Kalaycı¹,

Alexopoulos

Argon

et al. 2007

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.