Large-sample normality of the batch-means variance estimator

  • Authors:

  • Michael Sherman;David Goldsman

  • Affiliations:

  • Department of Statistics, Texas A&M University, College Station, TX 77843, USA;School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA

  • Venue:
  • Operations Research Letters
  • Year:
  • 2002

Quantified Score

Hi-index 0.00

Visualization

Abstract

Consider a stationary stochastic process, X"1,X"2,..., arising from a steady-state simulation. An important problem is that of estimating the expected value @m of the process. The usual estimator for @m is the sample mean based on n observations, X@?"n, and a measure of the precision of X@?"n is the variance parameter, @s^2=lim"n"-"~nVar[X@?"n]. This paper studies asymptotic properties of the batch-means estimator V@^"B(b,m) for @s^2 as both the batch size m and number of batches b become large. In particular, we give conditions for V@^"B(b,m) to converge to normality as m and b increase. Empirical examples illustrate our findings.