On the Minimax Nonparametric Detection of Signals in White Gaussian Noise

The article considers a minimax version of the problem of detection of a signal from a specified functional set $V$ in white Gaussian noise of intensity $\varepsilon>0$, under the condition that the signal energy is not less than a specified value $\rho(\varepsilon)>0$. Lower and upper bounds are obtained for the minimax detection efficiency, which are determined by characteristics of $V$ such as its internal radii and diameters at point 0. If $V$ is a set of functions of specified degree of smoothness, the resultant estimates make it possible to obtain necessary and sufficient conditions for asymptotically nontrivial or consistent minimax signal detection as $\varepsilon\to 0$.