On the stability of Bayes estimators for Gaussian processes (Q2266326)

Consider a Gaussian signal process \(X=(X_ t)\) observed in the presence of an additive Gaussian noise process \(N=(N_ t)\) for t in [0,T]. The paper is concerned with the behaviour of the Bayes estimator \(\delta_ 0\) under departures from Gaussian law by the prior or noise processes. The problem of choosing a suitable contamination model is discussed. Here the author chooses a QN-model, earlier introduced by \textit{A. F. Gualtierotti} [see C. R. Acad. Sci., Paris, Sér. A 288, 69-71 (1979; Zbl 0402.94003)]. Working in the framework of distributions on separable Banach spaces, the author derives upper bounds for the increase in the mean square error of \(\delta_ 0\) over the minimum possible mean square error under a QN-law prior or QN-law noise. It is shown that the performance of \(\delta_ 0\) is relatively close to optimal for small amounts of contamination.