Median-Based Estimates and Their Application in Controlling Reference Mark Stability
Publication: Journal of Surveying Engineering
Volume 136, Issue 2
Abstract
Control of reference mark stability is essential for monitoring of deformations of engineering structures or displacements of points in geodetic networks. Some robust estimates, which are based on median application, can be used for such purposes. For example, some R-estimates can be applied to determine displacements of geodetic points thus to identify unstable reference marks. However, such simplest approach can sometimes fail. Thus, a more complex strategy for monitoring of geodetic point stability is elaborated and presented in this paper. The concept presented here concerns leveling networks and applies some R-estimate and also other median-based estimates, i.e., the median distance to the median and the average distance to the median. The method proposed in this paper is illustrated with some practical examples and is compared with the traditional method for geodetic point stability monitoring.
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Acknowledgments
This research is supported by the Polish Ministry of Science and Higher Education under the grant “New methods of estimation of parameters in a functional model of geodetic observations ( estimation),” Grant No. UNSPECIFIEDN N526 255 734. The writer is very grateful to the reviewers of the paper for helpful suggestions and comments that have improved my manuscript significantly.
References
Chen, C. (2001). “Rank estimating equations for random effects models.” Stat. Probab. Lett., 54(1), 5–12.
Dionne, L. (1981). “Efficient nonparametric estimators of parameters in the general linear hypothesis.” Ann. Stat., 9(2), 457–460.
Duchnowski, R. (2003). “Generalized theory of VR-estimation in case of dependent observations.” Boll. Geod. Sci. Affini., 62(1), 17–32.
Duchnowski, R. (2008a). “Geodetic application of R-estimation: Leveling network examples.” Proc., 13th FIG Symp. on Deformation Measurement and Analysis and 4th Symp. on Geodesy for Geotechnical and Structural Engineering (CD-ROM), Laboratorio Nacional de Engenharia Civil, Lisbon, Portugal.
Duchnowski, R. (2008b). “R-estimation and its application to the LS adjustment.” Boll. Geod. Sci. Affini., 67(1), 21–30.
Feltovich, N. (2003). “Nonparametric tests of differences in medians: Comparison of the Wilcoxon-Mann-Whitney and robust rank-order tests.” Exp. Econ., 6(3), 273–297.
Huber, P. J. (1981). Robust statistics, Willey, New York.
Mukherjee, K., and Bai, Z. D. (2001). “R-estimation in autoregression with square-integrable score function.” J. Multivariate Anal., 81(11), 167–186.
Naranjo, J. D., and McKean, J. W. (1997). “Rank regression with estimated scores.” Stat. Probab. Lett., 33(2), 209–216.
Peiliang, X. (1989). “On robust estimation with correlated observations.” Bull. Geod., 63(3), 237–252.
Prószyński, W., and Kwaśniak, M. (2006). Basis of geodetic calculations of displacements. Notions and methodology elements, Oficyna Wydawnicza Politechniki Warszawskiej, Warsaw, Poland (in Polish).
Qingming, G, and Jinshan, L. (1999). “Generalized shrunken-type robust estimation.” J. Surv. Eng., 125(4), 177–184.
Rousseeuw, P. J., and Verboven, S. (2002). “Robust estimation in very small samples.” Comput. Stat. Data Anal., 40(4), 741–758.
Wiśniewski, Z. (1999). “A concept of robust estimation of variance coefficient (VR-estimation).” Boll. Geod. Sci. Affini., 58(3), 291–310.
Wiśniewski, Z. (2009). “Estimation of parameters in a split functional model of geodetic observation ( estimation).” J. Geodesy, Berlin, 83, 105–120.
Yang, Y. X. (1994). “Robust estimation for dependent observations.” Manuscr. Geod., 19(1), 10–17.
Yang, Y. X. (1997). “Estimators of covariance matrix at robust estimation based on influence functions.” ZFV. Z. Vermessungswes., 122(4), 166–174.
Yang, Y. X. (1999). “Robust estimation of geodetic datum transformation.” J. Geodesy, Berlin, 73(5), 268–274.
Yang, Y. X., Xu, T. H., and Song, L. J. (2005). “Robust estimation of variance components with application in global positioning system network adjustment.” J. Surv. Eng., 131(4), 107–112.
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Published In
Journal of Surveying Engineering
Volume 136 • Issue 2 • May 2010
Pages: 47 - 52
Copyright
© 2010 ASCE.
History
Received: Oct 30, 2008
Accepted: Jul 1, 2009
Published online: Jul 3, 2009
Published in print: May 2010
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