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On the Asymptotics of Constrained Local M-Estimators

Alexander Shapiro
The Annals of Statistics
Vol. 28, No. 3 (Jun., 2000), pp. 948-960
Stable URL: http://www.jstor.org/stable/2674061
Page Count: 13
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On the Asymptotics of Constrained Local M-Estimators
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Abstract

We discuss in this paper asymptotics of locally optimal solutions of maximum likelihood and, more generally, M-estimation procedures in cases where the true value of the parameter vector lies on the boundary of the parameter set S. We give a counterexample showing that regularity of S in the sense of Clarke is not sufficient for asymptotic equivalence of $\sqrt{n}$-consistent locally optimal M-estimators. We argue further that stronger properties, such as so-called near convexity or prox-regularity of S are required in order to ensure that any two $\sqrt{n}$-consistent locally optimal M-estimators have the same asymptotics.

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