We consider the problem of semiparametric estimation of functionals of the drift coefficient of a dynamical system by the observation of a non homogeneous diffusion process with small diffusion coefficient. Supposing that the drift coefficient is an unknown (smooth) function we propose a asymptotic minimax lower bound on the risk of all estimators and then we present asymptotically efficient estimators in the sense of this bound. The estimated integral-type functionals are defined with the help of the (unknown) solution of the deterministic limit dynamical system. Some particular and interesting functionals are presented as examples.
Semiparametric estimation of a functional of the drift coefficient for a non-homogeneous dynamical system with small noise / S.M. Iacus. - In: JOURNAL OF NONPARAMETRIC STATISTICS. - ISSN 1048-5252. - 13:1(2001), pp. 129-151. [10.1080/10485250008832846]
Semiparametric estimation of a functional of the drift coefficient for a non-homogeneous dynamical system with small noise
S.M. IacusPrimo
2001
Abstract
We consider the problem of semiparametric estimation of functionals of the drift coefficient of a dynamical system by the observation of a non homogeneous diffusion process with small diffusion coefficient. Supposing that the drift coefficient is an unknown (smooth) function we propose a asymptotic minimax lower bound on the risk of all estimators and then we present asymptotically efficient estimators in the sense of this bound. The estimated integral-type functionals are defined with the help of the (unknown) solution of the deterministic limit dynamical system. Some particular and interesting functionals are presented as examples.Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.