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In a general linear model, Y = X + R with Y and R n-dimensional, X a n p matrix, and p-dimensional, let be an M estimator of satisfying 0 = xᵢ (yᵢ - x'ᵢ). Let p such that (p n) ^3/2 /n 0. Then ᵢ|x'ᵢ (-) | P 0, and it is possible to find a uniform normal approximation for the distribution of under which arbitrary linear combinations a'ₙ (-) are asymptotically normal (when appropriately normalized) and (-) ' (X'X) (-) is approximately ²ₚ.
Stephen Portnoy (Sun,) studied this question.