New Method for Outlier Diagnostics in Linear Regression
Publication: Journal of Surveying Engineering
Volume 135, Issue 3
Abstract
The detection of the discordant points, i.e., outliers, in linear regression models is a problem, which has been studied extensively. Huber’s -estimation is recommended not only for robust regression but also for detecting outliers. However, -estimation does not show high performance in detecting outliers for some cases. The aim of this paper is to propose a new method for improving the ability of -estimation in outlier detection. It consists of the iterative combination of the -estimator along with a scheme of reducing weights in some observations at random. The theorems proving contribution of the proposed algorithms have also been included. A series of Monte Carlo simulation experiments show that the performance of the new algorithm in the presence of outliers is better than -estimation alone. By using the new method, the results, on average, improved by about 7%.
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Acknowledgments
The writers are very grateful to the editor and three anonymous reviewers for their valuable comments, which helped to improve the manuscript.
References
Applebaum, L. T. (1982). “Geodetic datum transformation by multiple regression equations.” Proc., 3rd Geodetic Symp. on Satellite Doppler Positioning, New Mexico State Univ., Las Cruces, N.M., 1, 207–223.
Baarda, W. (1968). A testing procedure for use in geodetic networks, Publication on Geodesy—New series, Vol. 2, No. 5, Netherlands Geodetic Commission, Delft, The Netherlands.
Barrodale, I., and Roberts, F. D. K. (1974). “Solution of an overdetermined system of equations in -norm.” Commun. ACM, 17, 319–320.
Baselga, S. (2007). “Global optimization solution of robust estimation.” J. Surv. Eng., 133(3), 123–128.
Baselga, S., and García-Asenjo, L. (2008). “GNSS differential positioning by robust estimation.” J. Surv. Eng., 134(1), 21–25.
Ferland, R. (2006). “Station coordinates time series discontinuities.” ITRF2005, ⟨ftp://macs.geod.nrcan.gc.ca/pub/requests/sinex/discontinuities⟩ (May 25, 2006).
Hadi, A. S., and Simonoff, J. S. (1993). “Procedures for the identification of multiple outliers in linear models.” J. Am. Stat. Assoc., 88(424), 1264–1272.
Hampel, F., Ronchetti, E., Rousseeuw, P., and Stahel, W. (1986). “Robust statistics: The approach based on influence functions.” Wiley series in probability and statistics, Wiley, New York.
Hekimoglu, S. (1997). “The finite sample breakdown points of the conventional iterative outlier detection procedures.” J. Surv. Eng., 123(1), 15–31.
Hekimoglu, S. (2005). “Do robust methods identify outliers more reliably than conventional tests for outliers?” Z. Geod. Geoinf. Landmanag., 130(3), 174–180.
Hekimoglu, S., and Erenoglu, R. C. (2007). “Effect of heteroscedasticity and heterogeneousness on outlier detection for geodetic networks.” J. Geodesy, Berlin, 81(2), 137–148.
Hekimoglu, S., and Koch, K. R. (1999). “How can reliability of the robust methods be measured?” Proc., 3rd Turkish-German Joint Geodetic Days, Vol. 1, M. O. Altan and L. Gründig, eds., Yildiz Technical Univ., Istanbul, Turkey, 179–196.
Hekimoglu, S., and Sanli, D. U. (2003). “Changing residuals by reweighting one or more observations.” Z. Geod. Geoinf. Landmanag., 128(4), 271–277.
Huber, P. J. (1981). “Robust statistics.” Wiley series in probability and statistics, Wiley, New York.
Koch, K. R. (1999). Parameter estimation and hypothesis testing in linear models, 2nd Ed., Springer, Berlin.
Krarup, T., Juhl, J., and Kubik, K. (1980). “Götterdämmerung over least squares adjustment.” Proc., 14th Congress of Int. Soc. Photogr., International Archives of Photogrammetry, Hamburg, Germany, 369–378.
NASA. (2004). “EGM96—The NASA GSFC and NIMA joint geopotential model.” ⟨http://cddis.nasa.gov/926/egm96/egm96.html⟩ (Aug. 6, 2008).
Pope, A. J. (1976). “The statistics of residuals and the detection of outliers.” NOAA Technical Rep. No. NOS65 NS1, National Geodetic Survey, Silver Spring, Md.
Rousseeuw, P. J., and Leroy, A. M. (1987). Robust regression and outlier detection, Wiley, New York.
Rousseeuw, P. J., and van Zomeren, B. C. (1990). “Unmasking multivariate outliers and leverage points.” J. Am. Stat. Assoc., 85(411), 633–639.
Williams, S. D. P. (2003). “The effect of coloured noise on the uncertainties of rates estimated from geodetic time series.” J. Geodesy, Berlin, 76(9–10), 483–494.
Williams, S. D. P., et al. (2004). “Error analysis of continuous GPS time series.” J. Geophys. Res., 109(B03412), 1–19.
Xu, P. L. (2005). “Sign-constrained robust least squares, subjective breakdown point and the effect of weights of observations on robustness.” J. Geodesy, Berlin, 79(1–3), 146–159.
Yang, Y. (1999). “Robust estimation of geodetic datum transformation.” J. Geod., 73(5), 268–274.
Zhang, J., et al. (1997). “Southern California permanent GPS geodetic array: Error analysis of daily position estimates and site velocities.” J. Geophys. Res., 102(B8), 18035–18055.
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© 2009 ASCE.
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Received: Mar 5, 2008
Accepted: Sep 26, 2008
Published online: Jul 15, 2009
Published in print: Aug 2009
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