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Semiparametrically weighted robust estimation of regression models

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  • Cízek, Pavel

Abstract

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.

Suggested Citation

  • Cízek, Pavel, 2011. "Semiparametrically weighted robust estimation of regression models," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 774-788, January.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:1:p:774-788
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    1. Čížek, Pavel, 2008. "General Trimmed Estimation: Robust Approach To Nonlinear And Limited Dependent Variable Models," Econometric Theory, Cambridge University Press, vol. 24(6), pages 1500-1529, December.
    2. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643, September.
    3. Ronchetti, Elvezio & Trojani, Fabio, 2001. "Robust inference with GMM estimators," Journal of Econometrics, Elsevier, vol. 101(1), pages 37-69, March.
    4. Mokkadem, Abdelkader, 1988. "Mixing properties of ARMA processes," Stochastic Processes and their Applications, Elsevier, vol. 29(2), pages 309-315, September.
    5. E ric E ngler & B ent N ielsen, 2009. "The empirical process of autoregressive residuals," Econometrics Journal, Royal Economic Society, vol. 12(2), pages 367-381, July.
    6. van Dijk, Dick & Franses, Philip Hans & Lucas, Andre, 1999. "Testing for ARCH in the Presence of Additive Outliers," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(5), pages 539-562, Sept.-Oct.
    7. Willems, Gert & Van Aelst, Stefan, 2005. "Fast and robust bootstrap for LTS," Computational Statistics & Data Analysis, Elsevier, vol. 48(4), pages 703-715, April.
    8. Balke, Nathan S & Fomby, Thomas B, 1994. "Large Shocks, Small Shocks, and Economic Fluctuations: Outliers in Macroeconomic Time Series," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 9(2), pages 181-200, April-Jun.
    9. Jonathan R. W. Temple, 1998. "Robustness tests of the augmented Solow model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(4), pages 361-375.
    10. Jung, Kang-Mo, 2005. "Multivariate least-trimmed squares regression estimator," Computational Statistics & Data Analysis, Elsevier, vol. 48(2), pages 307-316, February.
    11. Preminger, Arie & Franck, Raphael, 2007. "Forecasting exchange rates: A robust regression approach," International Journal of Forecasting, Elsevier, vol. 23(1), pages 71-84.
    12. Woo, Jaejoon, 2003. "Economic, political, and institutional determinants of public deficits," Journal of Public Economics, Elsevier, vol. 87(3-4), pages 387-426, March.
    13. Krishnakumar, J. & Ronchetti, E., 1997. "Robust estimators for simultaneous equations models," Journal of Econometrics, Elsevier, vol. 78(2), pages 295-314, June.
    14. Shinichi Sakata & Halbert White, 1998. "High Breakdown Point Conditional Dispersion Estimation with Application to S&P 500 Daily Returns Volatility," Econometrica, Econometric Society, vol. 66(3), pages 529-568, May.
    15. Andrews, Donald W.K., 1988. "Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables," Econometric Theory, Cambridge University Press, vol. 4(3), pages 458-467, December.
    16. Marc G. Genton & André Lucas, 2003. "Comprehensive definitions of breakdown points for independent and dependent observations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 81-94, February.
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    Cited by:

    1. Neykov, N.M. & Čížek, P. & Filzmoser, P. & Neytchev, P.N., 2012. "The least trimmed quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1757-1770.
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    3. Aquaro, M. & Čížek, P., 2013. "One-step robust estimation of fixed-effects panel data models," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 536-548.

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