Surprising phenomena in inference for iid p dimensional data for 0<p/n<1 and for p/n->oo
Surprising phenomena in inference for iid p dimensional data for 0<p/n<1 and for p/n->oo
Oct 6, 2014 1756 views 
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I.We study the behavior of robust regression and least squares in the unpenalized case for 0
oo the marginal distributions for almost all projections are asymptotically Gaussian so that non Gaussian empirical distributions suggest non linear phenomena. Suppose that the data are ,in fact , coordinatewise ,iid Gaussian, so that the distribution of all projections is Gaussian.We show that ,if p/n->oo , given any distribution F, a projection can be found whose empirical df is arbitrarily close to F. (with Boaz Nadler)