The Annals of Statistics

Achieving Information Bounds in Non and Semiparametric Models

Y. Ritov and P. J. Bickel

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 18, Number 2 (1990), 925-938.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176347633

Digital Object Identifier
doi:10.1214/aos/1176347633

Mathematical Reviews number (MathSciNet)
MR1056344

Zentralblatt MATH identifier
0722.62025

JSTOR
links.jstor.org

Subjects
Primary: 62G20: Asymptotic properties
Secondary: 62G05: Estimation

Keywords
Rate of convergence nonparametric estimations functionals of a density

Citation

Ritov, Y.; Bickel, P. J. Achieving Information Bounds in Non and Semiparametric Models. Ann. Statist. 18 (1990), no. 2, 925--938. doi:10.1214/aos/1176347633. https://projecteuclid.org/euclid.aos/1176347633


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