Statistical Inference on Covariance Structure and Sparse Discriminant Analysis

Tony Cai

Covariance structure is of fundamental importance in many areas of statistical inference and a wide range of applications, including genomics, fMRI analysis, risk management, and web search problems. In the high dimensional setting where the dimension p can be much larger than the sample size n, classical methods and results based on fixed p and large n are no longer applicable. In this talk, I will discuss some recent results on optimal estimation of covariance/precision matrices as well as sparse linear discriminant analysis with high-dimensional data. The results and technical analysis reveal new features that are quite different from the conventional low-dimensional problems.

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