Efficient robust estimation of time-series regression models

Abstract

Abstract. The 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 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 the cross-section and time-series data and prove the asymptotic normality and efficiency of the resulting procedure. A simulation study documents these theoretical properties in finite samples.

Facial Symmetry in Robust Anthropometrics*

“…The LWS‐based correlation coefficient r LWS with linearly decreasing or radial weights is computed using the weighted analogy of the approximative algorithm (29). The result with radial weights is even more robust than with linearly decreasing weights (31), because the radial weights assign smaller values to outlying pixels compared to the linearly decreasing weights. In any case, the LWS‐based method outperforms other correlation coefficients.…”