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June, 1987 $M$-Estimation for Discrete Data: Asymptotic Distribution Theory and Implications
Douglas G. Simpson, Raymond J. Carroll, David Ruppert
Ann. Statist. 15(2): 657-669 (June, 1987). DOI: 10.1214/aos/1176350367


The asymptotic distribution of an $M$-estimator is studied when the underlying distribution is discrete. Asymptotic normality is shown to hold quite generally within the assumed parametric family. When the specification of the model is inexact, however, it is demonstrated that an $M$-estimator whose score function is not everywhere differentiable, e.g., a Huber estimator, has a nonnormal limiting distribution at certain distributions, resulting in unstable inference in the neighborhood of such distributions. Consequently, smooth score functions are proposed for discrete data.


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Douglas G. Simpson. Raymond J. Carroll. David Ruppert. "$M$-Estimation for Discrete Data: Asymptotic Distribution Theory and Implications." Ann. Statist. 15 (2) 657 - 669, June, 1987.


Published: June, 1987
First available in Project Euclid: 12 April 2007

zbMATH: 0652.62011
MathSciNet: MR888432
Digital Object Identifier: 10.1214/aos/1176350367

Primary: 62E20
Secondary: 62F10 , 62G35

Keywords: $M$-estimator , discrete parametric model , robust estimation , smooth score function

Rights: Copyright © 1987 Institute of Mathematical Statistics

Vol.15 • No. 2 • June, 1987
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