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Eigenstructure in high dimensional random effects models

Presented by: 
Iain Johnstone Stanford University
Date: 
Monday 25th June 2018 - 11:00 to 11:45
Venue: 
INI Seminar Room 1
Abstract: 
The eigenstructure of i.i.d. samples from high dimensional data is known to show phenomena unexpected from experience with low dimensions -- eigenvalue spreading, bias and eigenvector inconsistency. Motivated by some problems in quantitative genetics, we now consider high dimensional data with more than one level of variation, and more specifically the spectral properties of estimators of the various components of variance matrices. We briefly describe bulk and edge eigenvalue distributions in this setting, and then focus more attention on properties and estimation of 'spiked' models. This is joint work with Zhou Fan and Yi Sun.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons