Abstract
We consider the problem of estimating an unknown parameter $\theta$ on the basis of independent identically distributed observations with a common density $f(x,\theta)$ and give some lower bounds for the accuracy of estimates of $\theta$ expressed in terms of the Hellinger distance $\rho(\theta; \theta') = \int_\mathscr{X} (f^{\frac{1}{2}}(x; \theta) - f^{\frac{1}{2}}(x; \theta'))^2 d\nu.$
Citation
R. Z. Hasminskii. I. A. Ibragimov. "On a Lower Bound for Moments of Point Estimators." Ann. Statist. 3 (1) 228 - 233, January, 1975. https://doi.org/10.1214/aos/1176343012
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