Suppose $n^{1/2}(\widehat{\theta}_{n}-\theta)\rightarrow \mathcal{N}_{p}(0,V(\theta))$ as *n**→**∞* for some estimate $\widehat{\theta}_{n}$ of *θ* in *R*^{p}. If *p*=1 and *g*(*θ*)=*∫*_{0}^{θ}*V*(*x*)^{−1/2}*dx*, it is well known that $n^{1/2}(g(\widehat{\theta}_{n})-g(\theta))\rightarrow \mathcal{N}(0,1)$ as *n**→**∞*, the distribution often being less skew so that inference based on the approximation $n^{1/2}(g(\widehat{\theta}_{n})-g(\theta))\sim \mathcal{N}(0,1)$should be more accurate than inference based on the approximation $V(\widehat{\theta}_{n})^{-1/2}n^{1/2}(\widehat{\theta}_{n}-\theta)\sim \mathcal{N}(0,1)$. If *p**>*1 there is generally no such one to one transformation *g*(*⋅*). We consider three different types of stabilization of *V*(*θ*). We also consider the problem of finding *g*(*⋅*) so that the components of $g(\widehat{\theta}_{n})$ are asymptotically independent.

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