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June, 1990 Achieving Information Bounds in Non and Semiparametric Models
Y. Ritov, P. J. Bickel
Ann. Statist. 18(2): 925-938 (June, 1990). DOI: 10.1214/aos/1176347633

Abstract

We consider in this paper two widely studied examples of nonparametric and semiparametric models in which the standard information bounds are totally misleading. In fact, no estimators converge at the $n^{-\alpha}$ rate for any $\alpha > 0$, although the information is strictly positive "promising" that $n^{-1/2}$ is achievable. The examples are the estimation of $\int p^2$ and the slope in the model of Engle et al. A class of models in which the parameter of interest can be estimated efficiently is discussed.

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Y. Ritov. P. J. Bickel. "Achieving Information Bounds in Non and Semiparametric Models." Ann. Statist. 18 (2) 925 - 938, June, 1990. https://doi.org/10.1214/aos/1176347633

Information

Published: June, 1990
First available in Project Euclid: 12 April 2007

zbMATH: 0722.62025
MathSciNet: MR1056344
Digital Object Identifier: 10.1214/aos/1176347633

Subjects:
Primary: 62G20
Secondary: 62G05

Rights: Copyright © 1990 Institute of Mathematical Statistics

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Vol.18 • No. 2 • June, 1990
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