Abstract
We consider the problem of testing the hypothesis that the parameter of linear regression model is 0 against an s-sparse alternative separated from 0 in the l2-distance. We show that, in Gaussian linear regression model with p < n, where p is the dimension of the parameter and n is the sample size, the non-asymptotic minimax rate of testing has the form \(\sqrt {\left( {s/n} \right)\log \left( {\sqrt p /s} \right)}\). We also show that this is the minimax rate of estimation of the l2-norm of the regression parameter.
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Russian Text © The Author(s), 2019, published in Avtomatika i Telemekhanika, 2019, No. 10, pp. 78–99.
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Carpentier, A., Collier, O., Comminges, L. et al. Minimax Rate of Testing in Sparse Linear Regression. Autom Remote Control 80, 1817–1834 (2019). https://doi.org/10.1134/S0005117919100047
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DOI: https://doi.org/10.1134/S0005117919100047