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 )
DOIONLINE Number - IJAECS-IRAJ-DOIONLINE-19745
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Published on 2023-08-24 |
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