Abstract:
We address the problem of detecting a sparse high-dimensional vector against
white Gaussian noise. An unknown vector is assumed to have only p nonzero components,
whose positions and sizes are unknown, the number p being on one hand large but on the
other hand small as compared to the dimension. The maximum likelihood (ML) test in this
problem has a simple form and, certainly, depends of $p$. We study statistical properties of
overparametrized ML tests, i.e., those constructed based on the assumption that the number
of nonzero components of the vector is $q (q>p)$ in a situation where the vector actually has
only p nonzero components. We show that in some cases overparametrized tests can be better
than standard ML tests.
Keywords:sparse vector, white Gaussian noise, maximum likelihood test.
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