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EigenPrism

swMATH ID: 21947
Software Authors: Janson, Lucas; Barber, Rina Foygel; Candès, Emmanuel
Description: EigenPrism: inference for high dimensional signal-to-noise ratios. Consider the following three important problems in statistical inference: constructing confidence intervals for the error of a high dimensional (p>n) regression estimator, the linear regression noise level and 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 l 2 -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 assumptions on coefficient sparsity or knowledge of the noise level. We investigate the width of the EigenPrism confidence intervals, including a comparison with a Bayesian setting in which our interval is just 5
Homepage: https://arxiv.org/pdf/1505.02097.pdf
Keywords: eigenprism; heritability; regression error; signal-to-noise ratio; variance estimation
Related Software: covTest; CorrT; selectiveInference; hdi; selective-inference; Eigenstrat; GitHub; MTG2; KBAL; sbw; ElemStatLearn; FASTCLIME; SetTest; multcomp; Bioconductor; R; CVX
Cited in: 16 Publications

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