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Asymptotic Theory For M-Estimators Over A Convex Kernel

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  • Arcones, Miguel A.

Abstract

We study the convergence in distribution of M-estimators over a convex kernel. Under convexity, the limit distribution of M-estimators can be obtained under minimal assumptions. We consider the case when the limit is arbitrary, not necessarily normal. If some Taylor expansions hold, the limit distribution is stable. As an application, we examine the limit distribution of M-estimators for the multivariate linear regression model. We obtain the distributional convergence of M-estimators for the multivariate linear regression model for a wide range of sequences of regressors and different types of conditions on the sequence of errors.

Suggested Citation

  • Arcones, Miguel A., 1998. "Asymptotic Theory For M-Estimators Over A Convex Kernel," Econometric Theory, Cambridge University Press, vol. 14(4), pages 387-422, August.
    • Handle: RePEc:cup:etheor:v:14:y:1998:i:04:p:387-422_14
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    Cited by:

    1. Nordhausen, Klaus & Oja, Hannu, 2011. "Multivariate L1 Statistical Methods: The Package MNM," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 43(i05).

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