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A central limit theorem applicable to robust regression estimators

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  • Portnoy, Stephen
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    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 22 (1987)
    Issue (Month): 1 (June)
    Pages: 24-50

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    Handle: RePEc:eee:jmvana:v:22:y:1987:i:1:p:24-50

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    Keywords: Central limit theorem robust regression asymptotics normal approximation;

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    Cited by:
    1. John C. Chao & Norman Rasmus Swanson, 2004. "Consistent Estimation with a Large Number of Weak Instruments," Yale School of Management Working Papers ysm374, Yale School of Management.
    2. Koenker, Roger & Machado, Jose A. F., 1999. "GMM inference when the number of moment conditions is large," Journal of Econometrics, Elsevier, vol. 93(2), pages 327-344, December.

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