Lower boundaries for parametric estimations in different norms
Statistics Theory
2014-07-17 v1 Statistics Theory
Abstract
We establish some new non-asymptotical lower bounds for deviation of regular unbiased estimation of unknown parameter from its true value in different norms, alike the classical Rao-Kramer's inequality. We show that if the new norm is weaker that ordinary Hilbertian norm, that the rate of convergence of arbitrary regular unbiased estimate does not exceed and if the new norm is stronger that one, the rate of convergence of the well-known Maximal Likelihood Estimate (MLE) is also equal to $ 1/\sqrt{n}.
Cite
@article{arxiv.1407.4182,
title = {Lower boundaries for parametric estimations in different norms},
author = {E. Ostrovsky and L. Sirota},
journal= {arXiv preprint arXiv:1407.4182},
year = {2014}
}