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- W3173220953 abstract "This paper treats two problems in high-dimensional testing that have receivedattention in the recent literature. The first problem is that tests based on aquadratic statistic (such as the Wald statistic) lose power against subspacesof the alternative hypothesis as the dimension of the parameter vector ofinterest increases. The second problem is that the Wald statistic is notdefined in high-dimensional settings, as it requires an invertible samplecovariance matrix. I simultaneously address these issues by generalizing theWald statistic to a statistic that is large in a subspace of the alternativehypothesis chosen by the econometrician. The existence of the statistic dependson a restricted eigenvalue condition that is tied directly to the size of thesubspace. I show that if the conventional sample covariance matrix is used,then the statistic can be computed using linear regression with a constantdependent variable, where coefficient vector is restricted to the subspace ofinterest. As a demonstration, I consider subspaces that contain sparse ornearly-sparse vectors. For these cases, the computation reduces to$ell_0$-regularized regression (best subset selection) and$ell_1$-regularized regression (Lasso), respectively." @default.
- W3173220953 created "2021-07-05" @default.
- W3173220953 creator A5019780673 @default.
- W3173220953 date "2019-07-11" @default.
- W3173220953 modified "2023-09-24" @default.
- W3173220953 title "Directing Power Towards Subspaces of the Alternative Hypothesis" @default.
- W3173220953 hasPublicationYear "2019" @default.
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