A central limit theorem applicable to robust regression estimators

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Abstract

Consider a general linear model, Y i =x′ i β+R i with R 1 , ..., R n i.i.d., β∈R p , and {x 1 , ..., x n } behaving like a random sample from a distribution in R p . Let β̂ be a robust M-estimator of β. To obtain an asymptotic normal approximation for the distribution of β̂ requires a Central Limit Theorem for W n = Σy i ψ(R i ), where y i = (X′X) -1 x i . When p→∞, previous results require p 5 n→0, but here a strong normal approximation for the distribution of W n in R p is provided under the condition (plogn) 3 2 n→0. © 1987.

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APA

Portnoy, S. (1987). A central limit theorem applicable to robust regression estimators. Journal of Multivariate Analysis, 22(1), 24–50. https://doi.org/10.1016/0047-259X(87)90073-X

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