Abstract
The delta method that consists of a Taylor approximation can be used to determine the asymptotic variance and distribution of test statistics. In an alternative approach, the test statistic can be combined with some estimating equations in the M-estimation framework for the purpose of deriving its asymptotic variance and distribution. Pierce (1982) uses this alternative approach and shows how the nuisance parameters can be replaced by their efficient estimators in deriving the asymptotic variance and distribution of certain test statistics. In this article, we show how these approaches are related for test statistics that can be written as the sample average of data.
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