Achieving Information Bounds in Non and Semiparametric Models
Ya'acov Ritov,Peter J. Bickel +1 more
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TLDR
In this article, the authors consider two widely studied examples of nonparametric and semiparametric models in which the standard information bounds are totally misleading, and show that no estimators converge at the $n−1/2−α−α$ rate for any α > 0, although the information is strictly positive "promising" that α ≥ 0.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.read more
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