ON ASYMPTOTICALLY MINIMAX NONPARAMETRIC DETECTION OF SIGNAL IN GAUSSIAN WHITE NOISE

摘要

For the problem of nonparametric detection of signal in Gaussian white noise, strong asymptotically minimax tests are found. The sets of alternatives are balls in the Besov space B_(2∞)~(s) with "small" balls in L_2 removed. The balls in the Besov space are defined in terms of orthogonal expansions of functions in trigonometrical basis. Similar result is also obtained for nonparametric hypothesis testing on a solution of ill-posed linear inverse problem with Gaussian random noise.