Generalized Shrunken-Type Robust Estimation
Publication: Journal of Surveying Engineering
Volume 125, Issue 4
Abstract
The parameter estimation problem in surveying adjustment is considered when outliers and multicollinearity exist simultaneously. A class of new estimators—generalized shrunken-type robust estimators—are proposed by grafting the biased estimation techniques philosophy into the robust estimator, and their statistical properties are discussed. By appropriate choices of the shrinking parameter matrix, we obtain many useful and important estimators. A numerical example is used to illustrate that these new estimators can not only resist the influence of outliers but also effectively overcome difficulty caused by multicollinearity.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Caspary, W., and Borutta, H. (1987). “Robust estimation in deformation models.” Survey Rev., 29, 29–45.
2.
Caspary, W., and Haen, W. (1990). “Simultaneous estimation of location and scale parameters in the context of robust M-estimation.” manuscr.geod., 15, 273–282.
3.
Gui, Q. M. (1997). “A new class of biased estimators in free net adjustment model.” Geomatics Res. Australasia, 66, 27–46.
4.
Gui, Q. M., and Dong, X. R. (1993). “A class of biased estimators for LN estimation problem.” manuscr.geod., 18, 1–9.
5.
Gui, Q. M., Huang, W. B., Zhang, J. J., and Yi, W. Y. (1997). “A class of biased estimators of parameters in rank-deficient Gauss-Markov model.” Acta Geodaetica et Cartographica Sinica, 26, 261–267.
6.
Gui, Q. M., and Zhang, J. J. (1998). “Robust biased estimation and its applications in geodetic adjustments.” J. Geodesy (in press).
7.
Gui, Q. M., Zhang, J. J., and Yi, W. Y. (1998). “Robust latent root estimation for adjustment parameters.” Chinese J. Zhengzhou Institute of Surveying and Mapping, 15, 8–12.
8.
Hampel, F. R., Ronchetti, E. M., Rousseeuw, P. J., and Stahel, W. A. (1986). Robust statistics, the approach based on influence functions. Wiley, New York.
9.
Hoerl, A. E., and Kennard, R. W. (1970). “Ridge regression: Biased estimation for non-orthogonal problems.” Technometrics, 12, 55–82.
10.
Huang, Y. C., and Mertikas, S. P. ( 1995). “On the design of robust regression estimators.” Manuscr. Geod., 20, 145–160.
11.
Huber, P. J. (1981). Robust statistics. Wiley, New York.
12.
Kaminski, W., and Wisniewski, Z. ( 1994). “The method of growing rigor for the adjustment of geodetic observations contaminated by gross errors.” Manuscr. Geod., 19, 55–61.
13.
Jia, Z. Z. (1987). “Combinative principal components estimate for regression parameters.” Chinese J. Math. Statis., and Appl. Prob., 2, 153–158.
14.
Koch, K. R. ( 1996). “Robuste Parameterschaetzung.” AVN, 103, 1–18.
15.
Massy, W. F. (1965). “Principal components regression in exploratory statistical research.” JASA, 60, 234–266.
16.
Nyquist, H. ( 1985). “Ridge type M-estimators.” Linear statistical inference, T. Calinski and W. Klonecki, eds., Springer, Berlin, 246–258.
17.
Wang, L. Q. (1990). “Generalized shrunken least squares estimators.” Chinese J. Appl. Prob. and Statist., 3, 225–232.
18.
Wang, S. G., and Chow, S. C. (1994). Advanced linear models: Theory and applications. Marcel Dekker, Inc., New York.
19.
Xia, J. L. (1988). “A kind of new biased estimator of regression parameters: Root root estimator.” Chinese J. Math. Statist. and Appl. Prob., 3, 21–30.
20.
Xu, P. L. (1989). “On robust estimation with correlated observation.” Bull. Geod., 63, 237–252.
21.
Xu, P. L., and Rummel, R. ( 1994). “Generalized ridge regression with applications in determination of potential fields.” Manuscr. Geod., 19, 8–21.
22.
Yang, H. (1989). “A single-parametric principal components regression estimator.” Appl. Math. J. Chinese Univ., 1, 74–80.
23.
Yang, Y. X. (1993). Robust estimation and its application in geodesy. Bayi Publishing House, Beijing.
24.
Yang, Y. X. ( 1994). “Robust estimation for dependent observations.” Manuscr. Geod., 19, 10–17.
25.
Yang, Y. X. (1997). “Estimators of covariance matrix at robust estimation based on influence functions.” ZfV, 122, 166–174.
26.
Zhow, J. W. (1989). “Classical theory of errors and robust estimation.” Acta Geodaetica et Cartographica Sinica, 18, 115–120.
Information & Authors
Information
Published In
Journal of Surveying Engineering
Volume 125 • Issue 4 • November 1999
Pages: 177 - 184
History
Received: Jun 8, 1998
Published online: Nov 1, 1999
Published in print: Nov 1999
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.