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Empirical evaluation of initial transient deletion rules for the steady-state mean estimation problem

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Abstract

We propose three new initial transient deletion rules (denoted H1, H2 and H3) to reduce the bias of the natural point estimator when estimating the steady-state mean of a performance variable from the output of a single (long) run of a simulation. Although the rules are designed for the estimation of a steady-state mean, our experimental results show that these rules may perform well for the estimation of variances and quantiles of a steady-state distribution. One of the proposed rules can be applied under the only assumption that the output of interest \(\{ Y(s): s\ge 0 \}\) has a stationary distribution whereas the other two rules require that \(Y(s)= f(X(s))\) for an \(\mathfrak {R}^d\)-valued Markov chain \(\{ X(s): s \ge 0 \}\). Our proposed rules are based on the use of sample quantiles and multivariate batch means to test the null hypothesis that a current observation Y(s) comes from a stationary distribution for \(\{ X(s): s \ge 0 \}\). We present experimental results to compare the performance of the new rules against three variants of the Marginal Standard Error Rule and the Glynn-Iglehart deletion rule. When the run length was sufficiently large to provide a reliable confidence interval for the estimated parameter, one of the proposed rules (H3) provided the best reductions in Mean Square Error, so that the identification of an underlying Markov chain X for which \(Y(s)= f(X(s))\) can be useful to determine an appropriate deletion point to reduce the initial transient, and one of our proposed rules (H2) can be useful to detect that a run length is too small to provide a reliable confidence interval.

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Acknowledgements

This research was supported by the Asociación Mexicana de Cultura A.C. and the National Council of Science of Technology of Mexico under Award Number 2018-000007-01EXTV-00092. The author acknowledges his gratitude to the Guest Editors and two anonymous Referees for their valuable comments and suggestions.

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  1. Department of Industrial & Operations Engineering, Instituto Tecnológico Autónomo de México, Rio Hondo 1, 01080, Mexico City, Mexico

    David F. Muñoz

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Muñoz, D.F. Empirical evaluation of initial transient deletion rules for the steady-state mean estimation problem. Comput Stat (2022). https://doi.org/10.1007/s00180-022-01243-2

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