A note on bias reduction

Withers, Christopher S.; Nadarajah, Saralees

doi:10.5802/crmath.49

Statistiques

A note on bias reduction

Withers, Christopher S.¹ ; Nadarajah, Saralees ²

¹ Industrial Research Limited, Lower Hutt, New Zealand
² University of Manchester, Manchester M13 9PL, UK

Comptes Rendus. Mathématique, Tome 358 (2020) no. 6, pp. 641-644.

Résumé

Let $\hat{w}$ be an unbiased estimate of an unknown $w \in R$ . Given a function $t (w)$ , we show how to choose a function $f_{n} (w)$ such that for $w^{*} = \hat{w} + f_{n} (w)$ , $E t (w^{*}) = t (w)$ . We illustrate this with $t (w) = w^{a}$ for a given constant $a$ . For $a = 2$ and $\hat{w}$ normal, this leads to the convolution equation $c_{r} = c_{r} \otimes c_{r}$ .

Reçu le : 2019-01-10
Accepté le : 2020-04-09
Publié le : 2020-10-02

DOI : 10.5802/crmath.49

Affiliations des auteurs :

Withers, Christopher S. ¹ ; Nadarajah, Saralees ²

¹ Industrial Research Limited, Lower Hutt, New Zealand
² University of Manchester, Manchester M13 9PL, UK

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     title = {A note on bias reduction},
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     pages = {641--644},
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     year = {2020},
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Withers, Christopher S.; Nadarajah, Saralees. A note on bias reduction. Comptes Rendus. Mathématique, Tome 358 (2020) no. 6, pp. 641-644. doi : 10.5802/crmath.49. http://www.numdam.org/articles/10.5802/crmath.49/

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