Abstract
In this paper we study the problem of estimating an unknown function f ϵ L2(0, 1) observed with some fractional Brownian noise. This problem is equivalent to estimation in the inverse problem of fractional integration. Since we are interested in boundary effects, we consider nonperiodic functions which belong to some Sobolev ball. Using a spline basis we construct an estimator and give its exact asymptotic risk. As an inverse problem this framework presents some interest. Indeed, the best basis for the functions is not the best one for the operator.
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