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M-Estimators Converging to a Stable Limit

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  • Arcones, Miguel A.

Abstract

We discuss the asymptotic linearization of multivariate M-estimators, when the limit distribution is stable. We consider two different types of kernels: VC and bracketing. When applied to the case of normal limits, our work improves the known results to obtain the limit distribution of M-estimators. We give weak conditions for the asymptotic normality of M-estimators over differentiable kernels. To obtain these results, we present an inequality on empirical processes satisfying a bracketing condition with respect to a norm smaller than the L2 norm.

Suggested Citation

  • Arcones, Miguel A., 2000. "M-Estimators Converging to a Stable Limit," Journal of Multivariate Analysis, Elsevier, vol. 74(2), pages 193-221, August.
    • Handle: RePEc:eee:jmvana:v:74:y:2000:i:2:p:193-221
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    References listed on IDEAS

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    1. Pollard, David, 1985. "New Ways to Prove Central Limit Theorems," Econometric Theory, Cambridge University Press, vol. 1(3), pages 295-313, December.
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    1. Volker Krätschmer & Henryk Zähle, 2017. "Statistical Inference for Expectile-based Risk Measures," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(2), pages 425-454, June.

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