Abstract
Suppose we have observations Yt = mt(θ) + et in ℝ for t = 1, 2, …, n where each mt = mt(θ) is a smooth function of an unknown vector θ, and the noise {et} is stationary with unknown marginals. We obtain asymptotic normality of the M-estimate θ with respect to any suitable smooth function ρ(e). Hence we obtain confidence regions for any smooth vector function t(θ) with ∂t(θ)/∂θ' of full rank. Extensions are given to the model Yt = mt(θ) + σt(θ)et in ℝ. Heuristic proofs are given.
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