Robust regression and outlier detection
Robust regression and outlier detection
Nonparametric econometrics
Computing LTS Regression for Large Data Sets
Data Mining and Knowledge Discovery
An evolutionary algorithm for robust regression
Computational Statistics & Data Analysis
The least trimmed quantile regression
Computational Statistics & Data Analysis
One-step robust estimation of fixed-effects panel data models
Computational Statistics & Data Analysis
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A class of two-step robust regression estimators that achieve a high relative efficiency for data from light-tailed, heavy-tailed, and contaminated distributions irrespective of the sample size is proposed and studied. In particular, the least weighted squares (LWS) estimator is combined with data-adaptive weights, which are determined from the empirical distribution or quantile functions of regression residuals obtained from an initial robust fit. Just like many existing two-step robust methods, the LWS estimator with the proposed weights preserves robust properties of the initial robust estimate. However, contrary to the existing methods and despite the data-dependent weights, the first-order asymptotic behavior of LWS is fully independent of the initial estimate under mild conditions. Moreover, the proposed estimation method is asymptotically efficient if errors are normally distributed. A simulation study documents these theoretical properties in finite samples; in particular, the relative efficiency of LWS with the proposed weighting schemes can reach 85%-100% in samples of several tens of observations under various distributional models.