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Efficient robust estimation of time-series regression models. (English) Zbl 1189.62140

Summary: This paper studies a new class of robust regression estimators based on the two-step least weighted squares (2S-LWS) estimator which employs data-adaptive weights determined from the empirical distribution or quantile functions of the regression residuals obtained from an initial robust fit. Just like many existing two-step robust methods, the proposed 2S-LWS estimator preserves robust properties of the initial robust estimate. However, contrary to the existing methods, the first-order asymptotic behavior of 2S-LWS is fully independent of the initial estimate under mild conditions. We propose data-adaptive weighting schemes that perform well both in cross-section and time-series data and prove the asymptotic normality and efficiency of the resulting procedures. A simulation study documents the theoretical properties in finite samples.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62F12 Asymptotic properties of parametric estimators
62F35 Robustness and adaptive procedures (parametric inference)
62L12 Sequential estimation
65C60 Computational problems in statistics (MSC2010)
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