On estimation of time dependent spatial signal in Gaussian white noise

P. -L. Chow, R. Khasminskii and R. Liptser

Stochastic Processes and their Applications, 2001, vol. 96, issue 1, 161-175

Abstract: We consider an estimation problem for time dependent spatial signal observed in a presence of additive cylindrical Gaussian white noise of a small intensity [var epsilon]. Under known a priori smoothness of the signal estimators with asymptotically the best in the mimimax sense risk convergence rate in [var epsilon] to zero are proposed. Moreover, on-line estimators for the signal and its derivatives in t are also created.

Keywords: Gaussian; random; measure; Kernel; estimator; Projection; estimator; On-line; estimator (search for similar items in EconPapers)
Date: 2001
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