Finite Sample Breakdown Points of Outlier Detection Procedures
Publication: Journal of Surveying Engineering
Volume 123, Issue 1
Abstract
The conventional iterative outlier detection procedures (CIODP), such as the Baarda-, Pope-, or t-testing procedure, based on the least-squares estimation (LSE) are used to detect the outliers in geodesy. Since the finite sample breakdown point (FSBP) of LSE is about 1/n, the FSBPs of the CIODP are also expected to be the same, about 1/n. In this paper, this problem is studied in view of the robust statistics for coordinate transformation with simulated data. Outliers have been examined in two groups: “random” and “jointly influential.” Random outliers are divided again into two subgroups: “random scattered” and “adjacent.” The single point displacements can be thought of as jointly influential outliers. These are modeled as the shifts along either the x- and y-axis or parallel to any given direction. In addition, each group is divided into two subgroups according to the magnitude of outliers: “small” and “large.” The FSBPs of either the Baarda-, Pope-, or t-testing procedure are the same and about 1/n. It means that only one outlier can be determined reliably by CIODP. However, the FSBP of the χ2-test is zero.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Baarda, W. (1968). “A testing procedure for use in geodetic networks.”Netherlands Geod Comm., Publ. on Geodesy, New Ser., 2(5).
2.
Caspary, W., and Borutta, H. (1987). “Robust estimation in deformation models.”Survey Rev., 29, 223(Jan.), 29–45.
3.
Chatterjee, S., and Hadi, A. S. (1988). Sensitivity analysis in linear regression. John Wiley & Sons, Inc., New York, N.Y.
4.
Chen, Y. Q., Kavouras, M., and Chrzanowski, A.(1987). “A strategy for detection of outlying observations in measurements of high precision.”The Can. Surveyor, 41, 529–540.
5.
Donoho, D. L., and Huber, P. J. (1983). “The notion of breakdown point.”a festschrift for Erich L. Lehmann, P. J. Bickel, K. A. Doksum, and J. L. Hodges Jr., eds., Wadsworth, Belmont, Calif., 157–184.
6.
Gao, Y., Krakiwsky, E., and Czompo, J. (1992). “Robust testing procedures for detection of multiple blunders.' J. Surv. Engrg., ASCE, 118(1), 11–23.
7.
Hadi, A. S., and Siminoff, J. S.(1993). “Procedures for the identification of multiple outliers in linear models.”J. Am. Statistical Assn., 88, 1264–1272.
8.
Hampel, F., Ronchetti, E., Rousseeuw, P., and Stahel, W. (1986). Robust statistics: the approach based on influence functions. John Wiley & Sons, Inc., New York, N.Y.
9.
Heck, B. (1981). “Der Einfluss eizelner Beobachtungen auf das Ergebnis einer Ausgleichung und die Suche nach Ausreissern in den Beobachtungen.”AVN 88, 17–34.
10.
Huber, P. J. (1981). Robust statistics. John Wiley & Sons, Inc., New York, N.Y.
11.
Kampmann, G. (1994). “Robuste deformation analyse mittels balancierter Ausgleichung.”AVN 1, 8–17.
12.
Koch, K. R. (1988). Parameter estimation and hypothesis testing in linear models. Springer-Verlag, New York, N.Y.
13.
Kok, J. J. (1984). “On data snooping and multiple outlier testing.”NOAA Tech. Rep. NOS NGS 30, Nat. Oc. Service, Nat. Geodetic Survey, U.S. Dept. of Commerce, Rockville, Md.
14.
Krarup, T., and Kubik, K. (1983). “The Danish method: experience and philosophy.”DGK, Reihe A, München, Germany, Heft 98.
15.
Markatou, J., and He, X.(1994). “Bounded influence and high breakdown point testing procedures in linear models.”J. Am. Statistical Assn., 89, 543–549.
16.
Öztürk, E., and Şerbetçi, M. (1992). Dengeleme Hesabi: cilt 3. KTÜ Genel Yayin No: 144, Trabzon.
17.
Pope, A. J. (1976). “The statistics of residuals and the detection of outliers.”NOAA Tech. Rep. NOS 65 NGS 1, U.S. Dept. of Commerce, Rockville, Md.
18.
Rousseeuw, P. J., and Leroy, A. M. (1987). Robust regression and outlier detection. John Wiley & Sons, Inc., New York, N.Y.
19.
Schwarz, C. R., and Kok, J. J. (1993). “Blunder detection and data snooping in LS and robust adjustments. J. Surv. Engrg., ASCE, 119(4), 128–136.
20.
Staudte, R. G., and Sheather, S. J. (1990). Robust estimation and testing. John Wiley & Sons, Inc., New York, N.Y.
21.
Xu, P. L. (1993). “Consequences of constant parameters and confidence intervals of robust estimation.”Anno LII-Bollettino Di Geodesia e Scienze Affini-N. 3.
22.
Ylvisaker, D.(1977). “Test resistance.”J. Am. Statistical Assn., 72, 551–557.
23.
Yohai, V. J.(1987). “High breakdown point and high efficiency robust estimates for regression.”The Ann. of Statistics, 15, 642–656.
Information & Authors
Information
Published In
Journal of Surveying Engineering
Volume 123 • Issue 1 • February 1997
Pages: 15 - 31
Copyright
Copyright © 1997 American Society of Civil Engineers.
History
Published online: Feb 1, 1997
Published in print: Feb 1997
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.