Previous |  Up |  Next


asymptotic efficiency; least weighted squares; robust regression; time series
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.
[1] Balke, N. S., Fomby, T. B.: Large shocks, small shocks, and economic fluctuations: outliers in macroeconomic time series. J. Appl. Econom. 9 (1994), 181-200. DOI 10.1002/jae.3950090205
[2] Čížek, P.: Least trimmed squares in nonlinear regression under dependence. J. Statist. Plann. Inference 136 (2006), 3967-3988. DOI 10.1016/j.jspi.2005.05.004 | MR 2299174 | Zbl 1103.62061
[3] Čížek, P.: General trimmed estimation: robust approach to nonlinear and limited dependent variable models. CentER discussion paper. Econom. Theory (to appear). MR 2456536
[4] Čížek, P.: Efficient robust estimation of regression models. CentER discussion paper Vol. 87. CentER Tilburg University Tilburg (2007).
[5] Genton, M. G., Lucas, A.: Comprehensive definitions of breakdown points for independent and dependent observations. J. R. Stat. Soc., Stat. Methodol. Ser. B 65 (2003), 81-94. DOI 10.1111/1467-9868.00373 | MR 1959094 | Zbl 1063.62038
[6] Gervini, D., Yohai, V. J.: A class of robust and fully efficient regression estimators. Ann. Stat. 30 (2002), 583-616. DOI 10.1214/aos/1021379866 | MR 1902900 | Zbl 1012.62073
[7] Mašíček, L.: Diagnostics and sensitivity of robust models. Unpublished Ph.D. Thesis Faculty of Mathematics and Physics, Charles University Prague (2004).
[8] Preminger, A., Franck, R.: Foreign exchange rates: a robust regression approach. Int. J. Forecasting 23 (2007), 71-84. DOI 10.1016/j.ijforecast.2006.04.009
[9] Rousseeuw, P. J.: Multivariate estimation with high breakdown point. Mathematical statistics and applications, Vol. B W. Grossman, G. Pflug, I. Vincze, W. Wertz Reidel Dordrecht (1985), 283-297. MR 0851060 | Zbl 0609.62054
[10] Rousseeuw, P. J., Leroy, A. M.: Robust Regression and Outlier Detection. John Wiley & Sons New York (1987). MR 0914792 | Zbl 0711.62030
[11] Sakata, S., White, H.: High breakdown point conditional dispersion estimation with application to S&P 500 daily returns volatility. Econometrica 66 (1998), 529-567. DOI 10.2307/2998574
[12] Temple, J. R. W.: Robustness tests of the augmented Solow model. J. Appl. Econometrics 13 (1998), 361-375. DOI 10.1002/(SICI)1099-1255(199807/08)13:4<361::AID-JAE483>3.0.CO;2-1
[13] Dijk, D. Van, Franses, P. H., Lucas, A.: Testing for ARCH in the presence of additive outliers. J. Appl. Econom. 14 (1999), 539-562. DOI 10.1002/(SICI)1099-1255(199909/10)14:5<539::AID-JAE526>3.0.CO;2-W
[14] Víšek, J. Á.: The least weighted squares II. Consistency and asymptotic normality. Bulletin of the Czech Econom. Soc. 9 (2002), 1-28.
[15] Víšek, J. Á.: Instrumental weighted variables. Austr. J. Stat. 35 (2006), 379-387.
[16] Woo, J.: Economic, political, and institutional determinants of public deficits. J. Public Economics 87 (2003), 387-426. DOI 10.1016/S0047-2727(01)00143-8
Partner of
EuDML logo