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Rates of Convergence of Minimum Distance Estimators and Kolmogorov's Entropy

Yannis G. Yatracos
The Annals of Statistics
Vol. 13, No. 2 (Jun., 1985), pp. 768-774
Stable URL: http://www.jstor.org/stable/2241209
Page Count: 7
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Rates of Convergence of Minimum Distance Estimators and Kolmogorov's Entropy
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Abstract

Let (X, A) be a space with a σ-field, M = {Ps; s ∈ Θ} be a family of probability measures on A with Θ arbitrary, X1, ⋯, Xn i.i.d. observations on Pθ. Define μn(A) = (1/n) ∑n i = 1 IA(Xi), the empirical measure indexed by A ∈ A. Assume Θ is totally bounded when metrized by the L1 distance between measures. Robust minimum distance estimators θ̂n are constructed for θ and the resulting rate of convergence is shown naturally to depend on an entropy function for Θ.

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