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Estimation in a problem of fractional integration. (English) Zbl 1064.62090

Summary: We study the problem of estimating an unknown function \(f\in L_2(0,1)\) 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.

MSC:

62M05 Markov processes: estimation; hidden Markov models
62M99 Inference from stochastic processes
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