# On Minimax Exponents of Sparse Testing

@article{Mukherjee2020OnME, title={On Minimax Exponents of Sparse Testing}, author={Rajarshi Mukherjee and Subhabrata Sen}, journal={arXiv: Statistics Theory}, year={2020} }

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…

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