But avar n n avar n n g c 2 g g c 1 g g c 2 c 1 g and

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But Avar n ̃ n  Avar n ̂ n  G C 2 G G C 1 G G  C 2 C 1  G and this is a psd matrix because C 2 C 1 is psd . 76
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The conclusion here is important and not surprising: If we have an asymptotically efficient estimator of , we should use it in constructing an estimator of g . The fact that smooth, nonlinear functions of are better estimated using an asymptotically more efficient estimator further illustrates the flexibility of asymptotic analysis. In finite-sample analysis, we can only be sure that linear functions of a parameter are better estimated (have smaller variance) using a best unbiased estimator. 77
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