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The Normal Approximation for Semiparametric Averaged Derivatives
P. M. Robinson
Abstract
With the same normalization as that for standard parametric statistics, and centered at a parameter of interest, many semiparametric estimates based on $n$ observations have been shown to be root-$n$-consistent and asymptotically normal. In the context of semiparametric averaged derivative estimates, we go further by showing that the rate of convergence of the finite-sample distribution to the normal limit distribution can equal that of standard parametric statistics.
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