Geodesic
On the Minimax Estimation Problem of a Fractional Derivative
Teoriâ veroâtnostej i ee primeneniâ, Tome 46 (2001) no. 4, pp. 658-677

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We consider the problem of minimax estimating the fractional derivative of the order $-\frac12$ of an unknown function in the Gaussian white noise model. This problem is closely related to the well-known Wicksell problem. In this paper the second-order minimax approach is developed.
Keywords: fractional derivative, second-order minimax risk, Wicksell problem. 
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     author = {G. K. Golubev and F. N. Enikeeva},
     title = {On the {Minimax} {Estimation} {Problem} of a {Fractional} {Derivative}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2001_46_4_a2/}
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G. K. Golubev; F. N. Enikeeva. On the Minimax Estimation Problem of a Fractional Derivative. Teoriâ veroâtnostej i ee primeneniâ, Tome 46 (2001) no. 4, pp. 658-677. http://geodesic.mathdoc.fr/item/TVP_2001_46_4_a2/