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arXiv · 1407.4182

Lower boundaries for parametric estimations in different norms

E. Ostrovsky·L. Sirota
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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 $ 1/\sqrt{n}, $ 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}.

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E. Ostrovsky, L. Sirota. 2014-07-16. Lower boundaries for parametric estimations in different norms. https://arxiv.org/abs/1407.4182

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