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Register a new userOn Minimax Exponents of Sparse Testing
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Added by
Subhabrata Sen
Publication date
2020
fields
Mathematical Statistics
and research's language is
English
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We consider exact asymptotics of the minimax risk for global testing against sparse alternatives in the context of high dimensional linear regression. Our results characterize the leading order behavior of this minimax risk in several regimes, uncovering new phase transitions in its behavior. This complements a vast literature characterizing asymptotic consistency in this problem, and provides a useful benchmark, against which the performance of specific tests may be compared. Finally, we provide some preliminary evidence that popular sparsity adaptive procedures might be sub-optimal in terms of the minimax risk.
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