Geodesic
Geometrical approach to the maximum likelihood estimation for infinite-dimensional Gaussian location.~I
Teoriâ veroâtnostej i ee primeneniâ, Tome 27 (1982) no. 2, pp. 388-395

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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. 
@article{TVP_1982_27_2_a24,
     author = {B. S. Cirel'son},
     title = {Geometrical approach to the maximum likelihood estimation for infinite-dimensional {Gaussian} {location.~I}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {388--395},
     publisher = {mathdoc},
     volume = {27},
     number = {2},
     year = {1982},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1982_27_2_a24/}
}
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B. S. Cirel'son. Geometrical approach to the maximum likelihood estimation for infinite-dimensional Gaussian location.~I. Teoriâ veroâtnostej i ee primeneniâ, Tome 27 (1982) no. 2, pp. 388-395. http://geodesic.mathdoc.fr/item/TVP_1982_27_2_a24/