Geodesic
On conistent hypothesis testing
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 23, Tome 442 (2015), pp. 48-74

Voir la notice de l'article provenant de la source Math-Net.Ru

We explore natural links between different types of consistency: consistency, uniform consistency and pointwise consistency. On the base of these results we provide both sufficient conditions and necessary conditions for existence of different types of consistent tests for the problems of hypothesis testing on a probability measure of independent sample, on a mean measure of Poisson process, on a solution of linear ill-posed problem in Gaussian noise, on a solution of deconvolution problem and for a signal detection in Gaussian white noise. In the last three cases we show that necessary conditions and sufficient conditions coincide. 
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     author = {M. S. Ermakov},
     title = {On conistent hypothesis testing},
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     pages = {48--74},
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     volume = {442},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2015_442_a2/}
}
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M. S. Ermakov. On conistent hypothesis testing. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 23, Tome 442 (2015), pp. 48-74. http://geodesic.mathdoc.fr/item/ZNSL_2015_442_a2/