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In the problem of signal detection in gaussian white noise we show asymptotic minimaxity of kernel-based tests. The test statistics equal $L_2$-norms of kernel estimates. The sets of alternatives are essentially nonparametric and are defined as the sets of all signals such that the $L_2$-norms of signal smoothed by the kernels exceed some constants ${\rho }_{ϵ}\>0$. The constant ${\rho }_{ϵ}$ depends on the power $ϵ$ of noise and ${\rho }_{ϵ}\to 0$ as $ϵ\to 0$. Similar statements are proved also if an additional information on a signal smoothness is given....

In the problem of signal detection in Gaussian white noise we show asymptotic minimaxity of kernel-based tests. The test statistics equal -norms of kernel estimates. The sets of alternatives are essentially nonparametric and are defined as the sets of all signals such that the -norms of signal smoothed by the kernels exceed some constants . The constant depends on the power of noise and as . Similar statements are proved also if an additional information on a...