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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(More)
We combine the formulation of Mandelbaum [Mandelbaum, A. (1986) Probab. Theory Rel. Fields 71, 129-147] with ideas from Whittle [Whittle, P. (1980) J. R. Stat. Soc. B 42, 143-149] to obtain a simple and constructive proof for the optimality of Gittins index processes in the general, nonmarkovian dynamic allocation (or "multi-armed bandit") problem. Our(More)
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