A note on bias reduction

Christopher S. Withers; Saralees Nadarajah

doi:10.5802/crmath.49

Statistiques

A note on bias reduction

Christopher S. Withers ¹ ; Saralees Nadarajah ²

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

Comptes Rendus. Mathématique, Volume 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 :

Christopher S. Withers ¹ ; Saralees Nadarajah ²

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

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {A note on bias reduction},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {641--644},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {6},
     year = {2020},
     doi = {10.5802/crmath.49},
     language = {en},
}

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Christopher S. Withers; Saralees Nadarajah. A note on bias reduction. Comptes Rendus. Mathématique, Volume 358 (2020) no. 6, pp. 641-644. doi : 10.5802/crmath.49. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.49/

Bibliographie
Cité par

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[2] Louis Comtet Advanced combinatorics: the art of finite and infinite expansions, Springer, 1974 | Zbl

[3] Kairat T. Mynbaev; Saralees Nadarajah; Christopher S. Withers; Aziza S. Aipenova Improving bias in kernel density estimation, Stat. Probab. Lett., Volume 94 (2014), pp. 106-112 | DOI | MR | Zbl

[4] Christopher S. Withers; Saralees Nadarajah Analytic bias reduction for $k$ -sample functionals, Sankhyā, Ser. A, Volume 70 (2008) no. 2, pp. 186-222 | MR | Zbl

[5] Christopher S. Withers; Saralees Nadarajah The bias and skewness of $M$ -estimators in regression, Electron. J. Stat., Volume 4 (2010), pp. 1-14 | DOI | MR | Zbl

[6] Christopher S. Withers; Saralees Nadarajah Bias-reduced estimates for skewness, kurtosis, $L$ -skewness and $L$ -kurtosis, J. Stat. Plann. Inference, Volume 141 (2011) no. 12, pp. 3839-3861 | DOI | MR | Zbl

[7] Christopher S. Withers; Saralees Nadarajah Bias reduction for the ratio of means, J. Stat. Comput. Simulation, Volume 81 (2011) no. 12, pp. 1799-1816 | DOI | MR | Zbl

[8] Christopher S. Withers; Saralees Nadarajah Estimates of low bias for the multivariate normal, Stat. Probab. Lett., Volume 81 (2011) no. 11, pp. 1635-1647 | DOI | MR | Zbl

[9] Christopher S. Withers; Saralees Nadarajah Reduction of bias and skewness with applications to second order accuracy, Stat. Methods Appl., Volume 20 (2011) no. 4, pp. 439-450 | DOI | MR | Zbl

[10] Christopher S. Withers; Saralees Nadarajah Nonparametric estimates of low bias, REVSTAT, Volume 10 (2012) no. 2, pp. 229-283 | MR | Zbl

[11] Christopher S. Withers; Saralees Nadarajah Calibration with low bias, Stat. Pap., Volume 54 (2013) no. 2, pp. 371-379 | DOI | MR | Zbl

[12] Christopher S. Withers; Saralees Nadarajah Delta and jackknife estimators with low bias for functions of binomial and multinomial parameters, J. Multivariate Anal., Volume 118 (2013), pp. 138-147 | DOI | MR | Zbl

[13] Christopher S. Withers; Saralees Nadarajah Density estimates of low bias, Metrika, Volume 76 (2013) no. 3, pp. 357-379 | DOI | MR | Zbl

[14] Christopher S. Withers; Saralees Nadarajah Bias reduction when data are rounded, Stat. Neerl., Volume 69 (2015) no. 3, pp. 236-271 | DOI | MR

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