Ontology highlight
ABSTRACT:
SUBMITTER: El Karoui N
PROVIDER: S-EPMC3767561 | biostudies-literature | 2013 Sep
REPOSITORIES: biostudies-literature
Proceedings of the National Academy of Sciences of the United States of America 20130816 36
We study regression M-estimates in the setting where p, the number of covariates, and n, the number of observations, are both large, but p ≤ n. We find an exact stochastic representation for the distribution of β = argmin(β∈ℝ(p)) Σ(i=1)(n) ρ(Y(i) - X(i')β) at fixed p and n under various assumptions on the objective function ρ and our statistical model. A scalar random variable whose deterministic limit rρ(κ) can be studied when p/n → κ > 0 plays a central role in this representation. We discover ...[more]