Efficient Robust Estimation via Two-Stage Generalized Empirical Likelihood
by Howard Bondell
Abstract: The triumvirate of outlier resistance, distributional robustness, and efficiency in both small and large samples, constitute the Holy Grail of robust statistics. We show that a two-stage procedure based on an initial robust estimate of scale followed by an application of generalized empirical likelihood comes very close to attaining that goal. The resulting estimators are able to attain full asymptotic efficiency at the Normal distribution, while simulations point to the ability to maintain this efficiency down to small sample sizes. Additionally, the estimators are shown to have the maximum attainable finite-sample replacement breakdown point, and thus remain stable in the presence of heavy-tailed distributions and outliers. Although previous proposals with full asymptotic efficiency exist in the literature, their finite sample efficiency can often be low. The method is discussed in detail for linear regression, but can be naturally extended to other areas, such as multivariate estimation of location and covariance.
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