Paper Title
Unconstrained Song Rule Advances Variance Estimators in Simulation Output Analysis

Abstract
The goal of this research is to estimate the variance of the sample mean in statistical experiments, including Monte Carlo simulation. To achieve this. Different methods have been used, such as the batch-means estmators (BME) with varying batch batch sizes, including To achieve this, different methods have been used, such as the batch-means estimator (BME) with varying batch sizes, including non-overlapping batch means (NBM) and overlapping batch means (OBM). Another method involves linearly combining two BMEs with large batch sizes to eliminate the bias constant. However, a recent study called the Song rule suggests that these methods may not be the optimal approach to minimize the mean squared error (mse). This paper introduces the unconstrained Song rule, which is similar to the Song rule but without the constraint that the two optimal weights must sum to 1. Estimating the two optimal weights in the unconstrained Song rule is more challenging than estimating one weight in the Song rule. However, the paper provides a version that can be implemented, which reduces the mse by over 20% for all cases studied compared to Song rule. The unconstrained Song rule is a significant advancement in the field of simulation output analysis. Keywords - Simulation, The Variance of the Sample Mean, Song Rule, Song Rule Smallest-Batch-Sizes Linear Combination.

Author - Wheyming Tina Song, Su Dong Hsun

Published : Volume-10,Issue-5  ( May, 2023 )

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