Third Annual 2015 Hartigan Lecture, Featured Speaker: Iain Johnstone @ 17 Hillhouse Avenue, 3rd Floor, Rm 328

Friday, December 11, 2015 - 3:00pm to 5:00pm
Stanford University
Likelihood ratios for eigenvalues in spiked multivariate models
In 1964 Alan James gave a remarkable classification of many of the eigenvalue distribution problems of multivariate statistics. We revisit the classification, now from the viewpoint of high dimensional models and low rank departures from the usual null hypotheses. For each of James' models, we describe the phase transition of the largest eigenvalue, and derive the asymptotic behavior of the likelihood ratios that correspond to null and alternative hypotheses about sub- and super-critical spikes. We find that the statistical experiment of observing the eigenvalues in the super-critical regime converges to a simple Gaussian shift. The story for the sub-critical regime is totally different: the experiment now converges to a Gaussian sequence model, and no optimal test about a sub-critical spike is available. (Joint work with Alexei Onatski and Prathapa Dharmawansa). Bio: Iain Johnstone is Marjorie Mhoon Fair Professor of Quantitative Science in the Department of Statistics at Stanford University. He holds a joint appointment in biostatistics in Stanford's School of Medicine. He received his Ph.D. in Statistics from Cornell in 1981. He has used ideas from harmonic analysis, such as wavelets, to understand noise-reduction methods in signal and image processing, and applied random matrix theory to the study of high-dimensional multivariate statistical methods, and collaborated extensively with investigators in cardiology and prostate cancer. Johnstone has been recipient of a Guggenheim Fellowship, Presidents’ Award from the Committee of Presidents of Statistical Societies, Alfred P. Sloan Research Fellowship, Presidential Young Investigator Award and Guy Medal in Bronze and Silver from the Royal Statistical Society. Johnstone is a member of the U.S. National Academy of Sciences and the American Academy of Arts and Sciences and a former president of the Institute of Mathematical Statistics and an adviser to the National Research Council, the National Science Foundation and the National Institutes of Health.