Testability of high-dimensional linear models with nonsparse structures.

ABSTRACT: Understanding statistical inference under possibly non-sparse high-dimensional models has gained much interest recently. For a given component of the regression coefficient, we show that the difficulty of the problem depends on the sparsity of the corresponding row of the precision matrix of the covariates, not the sparsity of the regression coefficients. We develop new concepts of uniform and essentially uniform non-testability that allow the study of limitations of tests across a broad set of alternatives. Uniform non-testability identifies a collection of alternatives such that the power of any test, against any alternative in the group, is asymptotically at most equal to the nominal size. Implications of the new constructions include new minimax testability results that, in sharp contr

SUBMITTER: Bradic J 

PROVIDER: S-EPMC9266975 | biostudies-literature | 2022 Apr

REPOSITORIES: biostudies-literature