CONFIDENCE INTERVAL ESTIMATION VIA BATCH MEANS AND TIME SERIES MODELING

KEEBOM KANG, Purdue University

Abstract

This research studies issues related to obtaining valid confidence intervals from steady state simulation output, with emphasis on using time series results in the batch means context. The focus of this research is on the statistical properties and the fundamental underlying structures of the batch means processes. The batch means process arising from an arbitrary autoregressive moving average (ARMA) time series is derived. As side results, the variance and correlation structures of the batch means process as functions of the batch size and the parameters of the original process are obtained. The parameters of the batch means process are numerically determined from those of the original process except for the first order ARMA process, for which a closed-form expression has been obtained. Computer graphics are used to visualize the relationships among numbers of batches, half widths, and coverages. Coverage contours and scatter diagrams that can be used as tools for evaluating the robustness of any confidence interval estimation procedures are developed. Coverage contours combine the ideas of the power function and the coverage function; both the half width and the coverage appear in one figure. Scatter diagrams, which exhibit the variability of confidence intervals, have been developed to supplement the coverage contours. The results on the batch means and the graphics are used for Monte Carlo investigation of the underlying structure of the batch means. Direct knowledge of the batch means process saves substantial computational effort. Issues related to the effects of asymmetry, dependence, and the asymptotic properties of batch means are also studied.

Degree

Ph.D.

Subject Area

Industrial engineering

COinS