A Linear Mini-max Estimator for the Case of a Quartic Loss Function
نویسندگان
چکیده
Let Y (t) be a stochastic process on [0; 1] modeled as dYt = (t)dt + dW (t), where W (t) denotes a standard Wiener process, and (t) is an unknown function assumed to belong to a given set L2[0; 1]. We consider the problem of estimating the value L( ), where L is a known continuous linear function de ned on , using linear estimators of the form hm; yi = R m(t)dY (t); m 2 L2[0; 1]. We solve the problem for the case of a quartic loss function, and compare the solution of the quartic case with the solution for the case of a quadratic loss function.
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