Open Access
2010 Stabilizing the asymptotic covariance of an estimate
Christopher Withers, Saralees Nadarajah
Electron. J. Statist. 4: 161-171 (2010). DOI: 10.1214/10-EJS562


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 Rp. If p=1 and g(θ)=0θV(x)1/2dx, 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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Christopher Withers. Saralees Nadarajah. "Stabilizing the asymptotic covariance of an estimate." Electron. J. Statist. 4 161 - 171, 2010.


Published: 2010
First available in Project Euclid: 4 February 2010

zbMATH: 1329.62112
MathSciNet: MR2645481
Digital Object Identifier: 10.1214/10-EJS562

Primary: 62G08 , 62G20

Keywords: asymptotic , Confidence regions , distribution-free , estimates , influence function , multivariate normal , stabilizing

Rights: Copyright © 2010 The Institute of Mathematical Statistics and the Bernoulli Society

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