A central limit theorem applicable to robust regression estimators

Stephen Portnoy

Journal of Multivariate Analysis, 1987, vol. 22, issue 1, 24-50

Abstract: Consider a general linear model, Yi=x'i[beta]+Ri with R1, ..., Rn i.i.d., [beta][set membership, variant]Rp, and {x1, ..., xn} behaving like a random sample from a distribution in Rp. Let [beta] be a robust M-estimator of [beta]. To obtain an asymptotic normal approximation for the distribution of [beta] requires a Central Limit Theorem for Wn = [Sigma]yi[psi](Ri), where yi = (X'X)-1xi. When p-->[infinity], previous results require p5/n-->0, but here a strong normal approximation for the distribution of Wn in Rp is provided under the condition (plogn)/3/2n-->0.

Keywords: Central; limit; theorem; robust; regression; asymptotics; normal; approximation (search for similar items in EconPapers)
Date: 1987
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