Properties of Batched Quadratic-Form Variance Parameter Estimators for Simulations

Christos Alexopoulos, David Goldsman, Gamze Tokol

INFORMS Journal on Computing · 2001 · Volume 13 · Issue 2

Abstract

We examine the practice of batching of certain quadratic-form estimators for the variance parameter of a stochastic process. The class of batched quadratic-form estimators includes, among others, the standardized time series (STS) weighted area and weighted Cramér-von Mises estimators. We give results on the expected value and variance of such estimators as the batch size and/or the number of batches increase. In particular, we show that the above STS estimators are consistent for the variance parameter in terms of mean squared error. An analytical example involving a first-order autoregressive process illustrates our findings.

Keywords

Simulation, Statistical Analysis

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