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September, 1984 Parametric Robustness: Small Biases can be Worthwhile
P. J. Bickel
Ann. Statist. 12(3): 864-879 (September, 1984). DOI: 10.1214/aos/1176346707


We study estimation of the parameters of a Gaussian linear model $\mathscr{M}_0$ when we entertain the possibility that $\mathscr{M}_0$ is invalid and a larger model $\mathscr{M}_1$ should be assumed. Estimates are robust if their maximum risk over $\mathscr{M}_1$ is finite and the most robust estimate is the least squares estimate under $\mathscr{M}_1$. We apply notions of Hodges and Lehmann (1952) and Efron and Morris (1971) to obtain (biased) estimates which do well under $\mathscr{M}_0$ at a small price in robustness. Extensions to confidence intervals, simultaneous estimation of several parameters and large sample approximations applying to nested parametric models are also discussed.


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P. J. Bickel. "Parametric Robustness: Small Biases can be Worthwhile." Ann. Statist. 12 (3) 864 - 879, September, 1984.


Published: September, 1984
First available in Project Euclid: 12 April 2007

zbMATH: 0545.62028
MathSciNet: MR751278
Digital Object Identifier: 10.1214/aos/1176346707

Primary: 62F10
Secondary: 62F25

Rights: Copyright © 1984 Institute of Mathematical Statistics


Vol.12 • No. 3 • September, 1984
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