Some statistical properties of the estimator associated with a variance reduction technique are presented. This technique is especially suitable in Monte-Carlo simulation studies in Statistics, e.g. in power estimation. The new estimator is unbiased. Its maximum likelihood variance estimator is negatively biased. Two new variance estimators, unbiased and nearly unbiased, are obtained. Two simulation studies are presented in order to illustrate the validity and usage of this variance reduction technique. © 1995.
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