This article is cited in 21 papers

Short Communications

Geometrical approach to the maximum likelihood estimation for infinite-dimensional Gaussian location. I

B. S. Cirel'son

Leningrad

Abstract: The MLE for the mean of the infinite-dimensional Gaussian measure with given covariance is studied; we assume that the mean belongs to a given set $V$ and relate the behaviour of MLE with the metric properties of $V$ (the metric is induced by the covariance). For example, a Hölder signal in the white noise admits the MLE if the Hölder exponent is greater than $1/2$ . Some inequalities for the distance between the mean and its MLE are given.

Received: 05.12.1978

 English version: Theory of Probability and its Applications, 1983, 27:2, 411–418

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