Geodesic
Minimax detection of signal in weighted Gaussian white noise
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 8, Tome 320 (2004), pp. 54-68

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We consider the problem of signal detection in weighted Gaussian white noise where the set of alternatives is essentially nonparametric. In this setting we find the family of asymptotically minimax tests. The results are extended on the case of tested parametric hypothesis versus nonparametric sets of alternatives. 
@article{ZNSL_2004_320_a3,
     author = {M. S. Ermakov},
     title = {Minimax detection of signal in weighted {Gaussian} white noise},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {54--68},
     publisher = {mathdoc},
     volume = {320},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_320_a3/}
}
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M. S. Ermakov. Minimax detection of signal in weighted Gaussian white noise. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 8, Tome 320 (2004), pp. 54-68. http://geodesic.mathdoc.fr/item/ZNSL_2004_320_a3/