Nonexistence of Rigorous Tests for Multiple Outlier Detection in Least-Squares Adjustment
Publication: Journal of Surveying Engineering
Volume 137, Issue 3
Abstract
The present paper focuses on the theory of outlier detection in least-squares adjustment. Although the case of a single outlier can be efficiently handled, extensions of the testing theory to the multiple outlier case seem questionable in rigor or applicability. This contribution is a demonstration that unambiguous determination of the vector of outliers from least-squares residuals is impossible without additional hypotheses. One such hypothesis, the single outlier hypothesis, is also proven to be sufficient (with just one exception) for the residual analysis to be conclusive in the process of outlier identification.
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Acknowledgments
The author acknowledges the editor and three anonymous reviewers for their constructive comments and suggestions that helped improve the original manuscript.
References
Baarda, W. (1968). “A testing procedure for use in geodetic networks.” Netherlands Geod. Comm., Publ. on Geodesy, 2(5)1–97.
Bernstein, D. S. (2009). Matrix mathematics: Theory, facts and formulas, 2nd Ed., Princeton University, Princeton, NJ.
Cen, M., Li, Z., Ding, X., and Zhuo, J. (2003). “Gross error diagnostics before least squares adjustment of observations.” J. Geodes., 77(9), 503–513.
Cross, P. A., and Price, D. R. (1985). “A strategy for the distinction between single and multiple gross errors in geodetic networks.” Manuscripta Geodaetica, 10(3), 172–178.
Ding, X., and Coleman, R. (1996). “Multiple outlier detection by evaluating redundancy contributions of observations.” J. Geodes., 70(8), 489–498.
Gui, Q., Gong, Y., Li, G., and Li, B. (2007). “A Bayesian approach to the detection of gross errors based on posterior probability.” J. Geodes., 81(10), 651–659.
Guo, J. F., Ou, J. K., and Wang, H. T. (2007). “Quasi-accurate detection of outliers for correlated observations.” J. Surv. Eng., 133(3), 129–133.
Huber, P. J. (1981). Robust statistics, Wiley, Hoboken, NJ.
Knight, N. L., Wang, J., and Rizos, C. (2010). “Generalised measures of reliability for multiple outliers.” J. Geodes., 84(10), 625–635.
Pope, A. J. (1976). “The statistics of residuals and the detection of outliers.” NOAA Tech. Rep. Nos. 65 NGS 1, U.S. National Geodetic Survey, Silver Spring, MD.
Xia, X. T., Wang, Z. Y., and Gao, Y. S. (2004). “Gross error detection using fuzzy-set theory.” Proc., 3rd Int. Symp. Instrumentation Science and Technology, Vol. 1, Xian, China, 120–127.
Xu, P. L. (2005). “Sign-constrained robust least squares, subjective breakdown point and the effect of weights of observations on robustness.” J. Geodes., 79(1-3), 146–159.
Information & Authors
Information
Published In
Journal of Surveying Engineering
Volume 137 • Issue 3 • August 2011
Pages: 109 - 112
Copyright
© 2011 American Society of Civil Engineers.
History
Received: Jul 8, 2010
Accepted: Oct 26, 2010
Published online: Dec 3, 2010
Published in print: Aug 1, 2011
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