Skart: A skewness- and autoregression-adjusted batch-means procedure for simulation analysis

Abstract

Skart is an automated sequential batch-means procedure for constructing a skewness- and autoregression-adjusted confidence interval (CI) for the steady-state mean of a simulation output process either in discrete time (i.e., using observation-based statistics), or in continuous time (i.e., using time-persistent statistics). Skart delivers a CI designed to satisfy user-specified requirements concerning both the CI's coverage probability and its absolute or relative precision. Skart exploits separate adjustments to the classical batch-means CI to account for the effects on the distribution of the underlying Student's t-statistic arising from skewness and autocorrelation of the batch means. The skewness adjustment is based on a Cornish–Fisher expansion for the classical batch-means t-statistic, and the autocorrelation adjustment is based on a first-order autoregressive approximation to the batch-means autocorrelation function. Skart also delivers a point estimator for the steady-state mean that is approximately free of initialization bias. The associated warm-up period is based on iteratively applying Von Neumann's randomness test to spaced batch means with increasing sizes for each batch and its preceding spacer. In extensive experimentation, Skart compared favorably with its competitors. [Supplementary material is available for this article. Go to the publisher's online edition of IIE Transactions for additional discussion, detailed proofs, etc.]

Keywords:

• Simulation
• statistical analysis
• steady-state analysis
• method of batch means
• Cornish–Fisher expansion
• autoregressive representation