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A central limit theorem applicable to robust regression estimators

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  • Portnoy, Stephen

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.

Suggested Citation

  • Portnoy, Stephen, 1987. "A central limit theorem applicable to robust regression estimators," Journal of Multivariate Analysis, Elsevier, vol. 22(1), pages 24-50, June.
    • Handle: RePEc:eee:jmvana:v:22:y:1987:i:1:p:24-50
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    Cited by:

    1. 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.
    2. John C. Chao & Norman R. Swanson, 2005. "Consistent Estimation with a Large Number of Weak Instruments," Econometrica, Econometric Society, vol. 73(5), pages 1673-1692, September.

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