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SUMMARY:Asymptotic Inference for Eigenstructure of Large Covariance Matric
 es - Jana Jankova (University of Cambridge)
DTSTART:20180625T134500Z
DTEND:20180625T143000Z
UID:TALK107368@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:A vast number of methods have been proposed in literature for 
 point estimation of eigenstructure of  covariance matrices in high-dimensi
 onal settings. In this work\, we study uncertainty quantification and prop
 ose methodology for inference and hypothesis testing for individual loadin
 gs of the covariance matrix. We base our methodology on a Lasso-penalized 
 M-estimator which\, despite non-convexity\, may be solved by a polynomial-
 time algorithm such as coordinate or gradient descent. Our results provide
  theoretical guarantees on asymptotic normality of the new estimators and 
 may be used for valid hypothesis testing and variable selection. These res
 ults are achieved under a sparsity condition relating the number of non-ze
 ro loadings\, sample size\, dimensionality of the covariance matrix and sp
 ectrum of the covariance matrix. This talk is based on joint work with Sar
 a van de Geer.
LOCATION:Seminar Room 1\, Newton Institute
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