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- W2286033046 abstract "We are concerned with minimax signal detection. In this setting, we discuss non-asymptotic and asymptotic approaches through a unified treatment. In particular, we consider a Gaussian sequence model that contains classical models as special cases, such as, direct, well-posed inverse and ill-posed inverse problems. Working with certain ellipsoids in the space of squared-summable sequences of real numbers, with a ball of positive radius removed, we compare the construction of lower and upper bounds for the minimax separation radius (non-asymptotic approach) and the minimax separation rate (asymptotic approach) that have been proposed in the literature. Some additional contributions, bringing to light links between non-asymptotic and asymptotic approaches to minimax signal, are also presented. An example of a mildly ill-posed inverse problem is used for illustrative purposes. In particular, it is shown that tools used to derive ‘asymptotic’ results can be exploited to draw ‘non-asymptotic’ conclusions, and vice-versa." @default.
- W2286033046 created "2016-06-24" @default.
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- W2286033046 date "2015-01-01" @default.
- W2286033046 modified "2023-09-26" @default.
- W2286033046 title "A unified treatment for non-asymptotic and asymptotic approaches to minimax signal detection" @default.
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- W2286033046 doi "https://doi.org/10.1214/15-ss112" @default.
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