Geodesic
On asymptotically efficient statistical inference on a~signal parameter
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 20, Tome 420 (2013), pp. 70-87

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We consider the problems of confidence estimation and hypothesis testing on a parameter of signal observed in Gaussian white noise. For these problems we point out lower bounds of asymptotic efficiency in the zone of moderate deviation probabilities. These lower bounds are versions of local asymptotic minimax Hajek–Le Cam lower bound in estimation and the lower bound for Pitman efficiency in hypothesis testing. The lower bounds were obtained for both logarithmic and sharp asymptotics of moderate deviation probabilities. 
@article{ZNSL_2013_420_a3,
     author = {M. S. Ermakov},
     title = {On asymptotically efficient statistical inference on a~signal parameter},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {70--87},
     publisher = {mathdoc},
     volume = {420},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2013_420_a3/}
}
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M. S. Ermakov. On asymptotically efficient statistical inference on a~signal parameter. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 20, Tome 420 (2013), pp. 70-87. http://geodesic.mathdoc.fr/item/ZNSL_2013_420_a3/