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The Statistics Department Seminar Series Presents: Zhou Fan, Stanford University

January 9, 2018 @ 4:10 pm - 5:00 pm

Room 411 West Hall

Zhou Fan

Department of Statistics
Stanford University


“Eigenvalues in multivariate random effects models ”


Random effects models are commonly used to measure genetic variance-covariance matrices of quantitative phenotypic traits in a population. The eigenvalues of these matrices describe the evolutionary response of the population to selection. However, they may be difficult to estimate from limited samples when the number of traits is large. I will discuss several phenomena concerning the eigenvalues of classical MANOVA estimators in such high-dimensional settings, including dispersion of the bulk eigenvalue distribution, bias and aliasing of large “spike” eigenvalues, and Tracy-Widom limits at the spectral edges. I will then describe a new statistical procedure that uses these results to consistently estimate the large population eigenvalues in a high-dimensional regime. The proofs develop and extend techniques in random matrix theory and free probability, which I will also briefly describe.
This is joint work with Iain M. Johnstone, Yi Sun, Mark W. Blows, and Emma Hine.


Tuesday January 9th, 2018 at 4:10pm in 411 West Hall
Welcome reception at 3:00pm
450 West Hall


January 9, 2018
4:10 pm - 5:00 pm


Room 411 West Hall
1085 S University Ave
Ann Arbor, MI 48109 United States
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