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Some strong limit theorems for M-estimators

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  • Arcones, Miguel A.

Abstract

Some laws of the iterated logarithm for empirical processes rescaled in the "time" parameter are presented. These laws of the iterated logarithm are applied to obtain strong limit theorems for M-estimators. In particular, a law of the iterated logarithm for M-estimators with unusual rates of convergence (in particular with cubic root asymptotics) is considered. We also obtain some Bahadur-Kiefer representations for M-estimators with unusual order.

Suggested Citation

  • Arcones, Miguel A., 1994. "Some strong limit theorems for M-estimators," Stochastic Processes and their Applications, Elsevier, vol. 53(2), pages 241-268, October.
    • Handle: RePEc:eee:spapps:v:53:y:1994:i:2:p:241-268
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    Cited by:

    1. Liebscher, Eckhard, 2003. "Strong convergence of estimators in nonlinear autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 84(2), pages 247-261, February.
    2. Miguel Arcones, 1998. "The Bahadur-Kiefer Representation of the Two Dimensional Spatial Medians," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(1), pages 71-86, March.
    3. Miguel Arcones, 1998. "Second Order Representations of the Least Absolute Deviation Regression Estimator," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(1), pages 87-117, March.

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