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Asymptotic Statistics by A.W. van der Vaart

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3

Delta Method

           The delta method consists of using a Taylor expansion to approximate a random vector of the form image by the polynomial image in Tn − θ. It is a simple but useful method to deduce the limit law of image from that of Tn − θ. Applications include the nonrobust-ness of the chi-square test for normal variances and variance stabilizing transformations.

3.1 Basic Result

Suppose an estimator Tn for a parameter θ is available, but the quantity ...

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