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In a variety of statistical problems, one is interested in the limiting distribution of statistics Tₙ = Tₙ (y₁, y₂, , yₙ; ₙ), where ₙ is an estimator of a parameter in the distribution of the yᵢ and where the limiting distribution of Tₙ = Tₙ (y₁, y₂, , yₙ;) is relatively easy to find. For cases in which the limiting distribution of Tₙ is normal with mean independent of, a useful method is given for finding the limiting distribution of Tₙ. A simple application to testing normality in regression models is given.
Donald A. Pierce (Tue,) studied this question.