## The Annals of Statistics

### Achieving Information Bounds in Non and Semiparametric Models

#### 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

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