Achieving Information Bounds in Non and Semiparametric Models
The Annals of Statistics · 1990 · Volume 18 · Issue 2
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.
Keywords
62G05, 62G20, functionals of a density, nonparametric estimations, rate of convergence
Enable JavaScript for citation tools and additional paper interactions.