Math 280: Multivariate Analysis from a Random Matrix Theory Perspective

A short course description.

We will use the Maple software package MOPS to do many calculations in multivariate statistics. Ioana Dumitriu will give some guest lectures on MOPS.

An overview of this course is Iain Johnstone's 2004 Wald Lecture (Part III). [pdf]

References for course:

1. R. J. Muirhead, Aspects of Multivariate Statistical Theory, Wiley, 1982.

2. I. M. Johnstone, On the distribution of the largest eigenvalue in principal component analysis, Annals of Statistics, 29 (2001), 295-327. [pdf]

3. C. A. Tracy and H. Widom, On orthogonal and symplectic matrix ensembles, Commun. Math. Phys. 177 (1996), 727-754 [pdf].

4. For an overview of the much broader issues that are involved, see the 2003 NSF report Statistics: Challenges and Opportunties for the Twenty-First Century.

Addendum:

1. Application of Random Matrix Theory to Multivariate Statistics by Momar Dieng and Craig Tracy.

2. High Dimensional Statistical Inference and Random Matrices, by Iain Johnstone.

3. Population Structure and Eigenanalysis, by Nick Patterson, Alkes L. Price and David Reich, PLOS Genetics, 2 (2006), 2074-2093.

4. A Tutorial on Multivariate Statistical Analysis, lecture by Craig Tracy at SAMSI, Program on High Dimensional Inference and Random Matrices, Opening Workshop.

5. Multivariate Analysis and Jacobi Ensembles: Largest eigenvalue, Tracy Widom Limits and Rate of Convergence by Iain Johnstone.