Adaptive filtering of a random signal in Gaussian white noise

Eduard N. Belitser, Farida N. Enikeeva

Abstract: We consider the problem of estimating an infinite-dimensional vector θ observed in Gaussian white noise. Under the condition that components of the vector have a Gaussian prior distribution that depends on an unknown parameter β, we construct an adaptive estimator with respect to β. The proposed method of estimation is based on the empirical Bayes approach.