Non-parametric lower bounds and information functions

Novak, Serguei (2018) Non-parametric lower bounds and information functions. In: ISNPS-Third Conference of the International Society for Nonparametric Statistics (ISNPS), 11-16 June 2016, Avignon, France.

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Abstract

We argue that common features of non-parametric estimation appear in parametric cases as well if there is a deviation from the classical regularity condition. Namely, in many non-parametric estimation problems (as well as some parametric cases) unbiased finite-variance estimators do not exist; neither estimator converges locally uniformly with the optimal rate; there are no asymptotically unbiased with the optimal rate estimators; etc..
We argue that these features naturally arise in particular parametric subfamilies of non-parametric classes of distributions. We generalize the notion of regularity of a family of distributions and present a general regularity condition, which leads to the notions of the information index and the information function.
We argue that the typical structure of a continuity modulus explains why unbiased finite-variance estimators cannot exist if the information index is larger than two, while in typical non-parametric situations neither estimator converges locally uniformly with the optimal rate. We present a new result on impossibility of locally uniform convergence with the optimal rate.

Item Type: Conference or Workshop Item (Lecture)
Additional Information: Novak S.Y. (2016) Non-parametric lower bounds and information functions. – In: Abstr. ISNPS-3 Conf., Avignon, p. 131.
Research Areas: A. > School of Science and Technology > Design Engineering and Mathematics
Item ID: 20799
Notes on copyright: Final Accepted Version: This is a pre-copyedited version of a contribution published in Nonparametric Statistics: 3rd ISNPS, Avignon, France, June 2016, Editors: Patrice Bertail, Pierre-André Cornillon, Eric Matzner-Lober, Delphine Blanke, published by Springer International Publishing. The definitive authenticated version is available online via https://doi.org/10.1007/978-3-319-96941-1
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Depositing User: Serguei Novak
Date Deposited: 25 Oct 2016 10:21
Last Modified: 25 May 2019 16:59
URI: https://eprints.mdx.ac.uk/id/eprint/20799

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