January 23: Pk Sen
"Robust Statistical Inference for High-Dimension Low Sample Size Models with Application to Genomics"
In high-dimension (K) low sample size (n) environments, nonlinear, inequality, order, or general shape constraints often crop up in rather complex ways. As a result, likelihood principles based optimal statistical inference procedures either may not be in a closed, manageable form or even may not exist. While some of these complex statistical inference
problems can be treated in suitable asymptotic setups, the curse of dimensionality (i.e. K > > n, possibly small) calls for a different asymptotics route (K very large) having different perspectives. Roy?s (1953) union-intersection principle, with genesis in the likelihood principle, provides some alternative approaches which are generally more amenable for the K > > n environments. This scenario is appraised with twoimportant applications in genomics where a large number (K) of genes with plausible dependence as well as heterogeneity amidst a small sample size environment creates impasses for standard robust statistical inference. These statistical perspectives are appraised in
some nonstandard ways.