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 Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year EigenPrism: inference for high dimensional signal-to-noise ratios. Zbl 1373.62355Janson, Lucas; Barber, Rina Foygel; Candès, Emmanuel 2017 all top 5 Cited by 30 Authors 2 Bradic, Jelena 2 Candès, Emmanuel J. 2 Foygel Barber, Rina 2 Guo, Zijian 2 Zhu, Yinchu 1 Azriel, David 1 Cai, Tony Tony 1 Collier, Olivier 1 Comminges, Laetitia 1 Fan, Jianqing 1 Gamarnik, David 1 Gassiat, Elisabeth 1 Holmes, Susan P. 1 Janson, Lucas 1 Javanmard, Adel 1 Law, Michael 1 Li, Hongzhe 1 Montanari, Andrea 1 Ndaoud, Mohamed 1 Ritov, Ya’acov 1 Schwartzman, Armin 1 Tsybakov, Alexandre B. 1 Verzelen, Nicolas 1 Wang, Rui 1 Wang, Wanjie 1 Wang, Zhaoliang 1 Xu, Xingzhong 1 Xue, Liugen 1 Zadik, Ilias 1 Zhao, Qingyuan all top 5 Cited in 8 Serials 7 The Annals of Statistics 2 Bernoulli 2 Electronic Journal of Statistics 1 Journal of the American Statistical Association 1 Communications in Statistics. Theory and Methods 1 Bulletin of the American Mathematical Society. New Series 1 Statistical Papers 1 Journal of the Royal Statistical Society. Series B. Statistical Methodology Cited in 4 Fields 16 Statistics (62-XX) 1 Probability theory and stochastic processes (60-XX) 1 Computer science (68-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year