Previous |  Up |  Next


robust regression; autocorrelated errors; heteroscedastic regression; instrumental variables; least weighted squares
Highly robust statistical and econometric methods have been developed not only as a diagnostic tool for standard methods, but they can be also used as self-standing methods for valid inference. Therefore the robust methods need to be equipped by their own diagnostic tools. This paper describes diagnostics for robust estimation of parameters in two econometric models derived from the linear regression. Both methods are special cases of the generalized method of moments estimator based on implicit weighting of individual observations. This has the effect of down-weighting less reliable observations and ensures a high robustness and low sub-sample sensitivity of the methods. Firstly, for a robust regression method efficient under heteroscedasticity we derive the Durbin–Watson test of independence of random regression errors, which is based on the approximation to the exact null distribution of the test statistic. Secondly we study the asymptotic behavior of the Durbin–Watson test statistic for the weighted instrumental variables estimator, which is a robust analogy of the classical instrumental variables estimator.
[1] Aitken, A. C.: On least squares and linear combination of observations. Proc. Roy. Statist. Soc. 55 (1935), 42–48. Zbl 0011.26603
[2] Čížek, P.: Efficient robust estimation of time-series regression models. Appl. Math. 53 (2008), 267–279. DOI 10.1007/s10492-008-0009-x | MR 2411129 | Zbl 1189.62140
[3] Cohen-Freue, G. V., Zamar, R. H.: A robust instrumental variables estimator. J. Roy. Statist. Soc. (2011), (submitted).
[4] Cragg, J. G.: More efficient estimation in the presence of heteroscedasticity of unknown form. Econometrica 51 (1938), 751–763. DOI 10.2307/1912156 | MR 0712368
[5] Durbin, J., Watson, G. S.: Testing for serial correlation in least squares regression I. Biometrika 37 (1950), 409–428. MR 0039210 | Zbl 0039.35803
[6] Durbin, J., Watson, G. S.: Testing for serial correlation in least squares regression II. Biometrika 38 (1951), 159–178. MR 0042662 | Zbl 0042.38201
[7] Farebrother, R. W.: Pan’s procedure for the tail probabilities of the Durbin-Watson statistic. Appl. Stat. 29 (1980), 224–227. DOI 10.2307/2986316 | Zbl 0475.62044
[8] Gagliardini, P., Trojani, F., Urga, G.: Robust GMM tests for structural breaks. Journal of Econometrics 129 (2005), 139–182. DOI 10.1016/j.jeconom.2004.09.006 | MR 2209661
[9] Greene, W. H.: Econometric analysis. Macmillan, New York, 2002, Fifth edition.
[10] Hansen, L. P.: Large samples properties of generalized method of moments estimators. Econometrica 50 (1982), 1029–1054. DOI 10.2307/1912775 | MR 0666123
[11] Hekimoglu, S., Erenoglu, R. C., Kalina, J.: Outlier detection by means of robust regression estimators for use in engineering science. Journal of Zhejiang University Science A 10 (2009), 909–921. DOI 10.1631/jzus.A0820140 | Zbl 1178.62015
[12] Jurečková, J., Picek, J.: Robust statistical methods with R. Chapman & Hall/CRC, Boca Raton, 2006. MR 2191689 | Zbl 1097.62020
[13] Jurečková, J., Sen, P. K.: Robust statistical procedures. Asymptotics and interrelations. Wiley, New York, 1996. MR 1387346
[14] Kalina, J.: On multivariate methods in robust econometrics. Prague economic papers 2011, (accepted, in print).
[15] Kalina, J.: Robust image analysis of faces for genetic applications. Eur. J. Biomed. Inf. 6, 2 (2010), 6–13.
[16] Kalina, J.: Asymptotic Durbin-Watson test for robust regression. Bull. Int. Statist. Inst. 62 (2007), 3406–3409.
[17] Ortelli, C., Trojani, F.: Robust efficient method of moments. Journal of Econometrics 128 (2005), 69–97. DOI 10.1016/j.jeconom.2004.08.008 | MR 2022927
[18] Rao, C. R.: Linear methods of statistical induction and their applications. Wiley, New York, 1973, Second edition. MR 0346957
[19] Rousseuw, P. J., Leroy A. M.: Robust regression and outlier detection. Wiley, New York, 1987. MR 0914792
[20] Rousseeuw, P. J., van Driessen, K.: Computing LTS regression for large data sets. Data Mining and Knowledge Discovery 12 (2006), 29–45. DOI 10.1007/s10618-005-0024-4 | MR 2225526
[21] Sakata, S., White, H.: S-estimation of nonlinear regression models with dependent and heterogeneous observations. Journal of Econometrics 103 (2001), 5–72. DOI 10.1016/S0304-4076(01)00039-2 | MR 1838195 | Zbl 0998.62060
[22] Víšek, J. Á.: Robust error-term-scale estimate. In: Antoch, J., Hušková, M., Sen, P. K. (eds.) Nonparametrics and robustness in modern statistical inference and time series analysis, IMS Collections 7, Institute of Mathematical Statistics, Beachwood, Ohio, 2010, 254–267. MR 2808385
[23] Víšek, J. Á.: Instrumental weighted variables. Austrian J. Statist. 35 (2006), 379–387.
[24] Víšek, J. Á.: Robustifying generalized method of moments. In: Kupka, K. (ed.) Data analysis 2004/II, Progressive methods of statistical data analysis and modelling for research and technical practice, Trilobyte Statistical Software, Pardubice, 2005, 171–193.
[25] Víšek, J. Á.: Regression with high breakdown point. In: Antoch, J., Dohnal, G. (eds.) Proceedings of ROBUST 2000, Summer School of JČMF, JČMF and Czech Statistical Society, 2001, 324–356.
[26] Wooldridge, J. M.: Applications of generalized method of moments estimation. J. Econ. Perspect. 15, 4 (2001), 87–100. DOI 10.1257/jep.15.4.87
Partner of
EuDML logo