Non-parametric lower bounds and information functions
Novak, Serguei 
ORCID: https://orcid.org/0000-0001-7929-7641
(2018)
Non-parametric lower bounds and information functions.
Nonparametric Statistics: 3rd ISNPS, Avignon, France, June 2016.
In: ISNPS-Third Conference of the International Society for Nonparametric Statistics (ISNPS), 11-16 June 2016, Avignon, France.
ISBN 9783319969404.
ISSN 2194-1009
[Conference or Workshop Item]
(doi:10.1007/978-3-319-96941-1)
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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 |
| Useful Links: | |
| Depositing User: | Serguei Novak |
| Date Deposited: | 25 Oct 2016 10:21 |
| Last Modified: | 29 Nov 2022 19:34 |
| URI: | https://eprints.mdx.ac.uk/id/eprint/20799 |
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