EigenPrism: inference for high dimensional signal-to-noise ratios.

ABSTRACT: Consider the following three important problems in statistical inference, namely, constructing confidence intervals for (1) the error of a high-dimensional (p > n) regression estimator, (2) the linear regression noise level, and (3) the genetic signal-to-noise ratio of a continuous-valued trait (related to the heritability). All three problems turn out to be closely related to the little-studied problem of performing inference on the [Formula: see text]-norm of the signal in high-dimensional linear regression. We derive a novel procedure for this, which is asymptotically correct when the covariates are multivariate Gaussian and produces valid confidence intervals in finite samples as well. The procedure, called EigenPrism, is computationally fast and makes no assumptio

SUBMITTER: Janson L 

PROVIDER: S-EPMC5663223 | biostudies-literature | 2017 Sep

REPOSITORIES: biostudies-literature