Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Testability of high-dimensional linear models with non-sparse structures   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 contrast to the current results,
do not depend on the sparsity of the regression parameters. We identify new
tradeoffs between testability and feature correlation. In particular, we show
that, in models with weak feature correlations, minimax lower bound can be
attained by a test whose power has the $\sqrt{n}$ rate, regardless of the size
of the model sparsity.

23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn