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June 1999 Target estimation for bias and mean square error reduction
Javier Cabrera, Luisa Turrin Fernholz
Ann. Statist. 27(3): 1080-1104 (June 1999). DOI: 10.1214/aos/1018031269


Given a statistical functional T and a parametric family of distributions, a bias reduced functional $\tilde{T}$ is defined by setting the expected value of the statistic equal to the observed value. Under certain regularity conditions this new statistic, called the target estimator, will have smaller bias and mean square error than the original estimator. The theoretical aspects are analyzed by using higher order von Mises expansions. Several examples are given, including $M$-estimates of location and scale. The procedure is applied to an autoregressive model, the errors-in-variables model and the logistic regression model. A comparison with the jackknife and the bootstrap estimators is also included.


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Javier Cabrera. Luisa Turrin Fernholz. "Target estimation for bias and mean square error reduction." Ann. Statist. 27 (3) 1080 - 1104, June 1999.


Published: June 1999
First available in Project Euclid: 5 April 2002

zbMATH: 0986.62013
MathSciNet: MR1724042
Digital Object Identifier: 10.1214/aos/1018031269

Primary: 62G99
Secondary: 62E20

Keywords: bias , Mean square error , parametric family , Statistical functionals , target estimates , von Mises expansions

Rights: Copyright © 1999 Institute of Mathematical Statistics


Vol.27 • No. 3 • June 1999
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