Research Article
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Year 2023, Volume: 8 Issue: 1, 26 - 31, 15.02.2023

Hasan Dilmaç , Yasemin Şişman

https://doi.org/10.26833/ijeg.996340

Abstract

References

  • Fan, H. (1997). Theory of errors and least squares adjusment. Royal Instıtute of Technology, 72, 100-44, Stockholm, Sweden.
  • Ingram, E. L. (1911). Geodetic surveying and the adjustment of observations (methods of least squares). McGraw-Hill Book Company, Inc. 370 Seventh Avenue, New York.
  • Ghilani, C. D. (2017). Adjustment computations: Spatial data analysis (Sixth edition). John Wiley ve Sons, Inc., Hoboken, New Jersey.
  • Mikhail, E. M. & Ackermann, F. E. (1976). Observations and least squares. Thomas Y. Crowell Company, Inc. 666 Fifth Avenue, New York.
  • Čížek, P. & Víšek, J. Á. (2005). Least Trimmed Squares. XploRe®—Application Guide,49-63. Springer, Berlin, Heidelberg.doi: 10.1007/978-3-642-57292-0_2
  • Rousseeuw, J. R. & Leroy, A. M. (1987). Robust Regression and Outlier Detection. John Wiley ve Sons, Inc.
  • Hekimoglu, S. (2005). Do Robust Methods Identify Outliniers More Reliably Than Conventional Tests for Outliniers? Zeitschrift für Vermessungwesen, 3, 174-180.
  • Baarda, W. (1968). A testing procedure for use in geodetic networks. Netherlands Geodetic Com., New Series, Delft, Netherlands, 2(5).
  • Pope, A. J. (1976). The statistics of residuals and the detection of outliers. NOAA Technical Report. NOS 65 NGS 1, U. S. Dept. of Commerce, Rockville, Md.
  • Koch, K. R. (1999). Parameter Estimation and Hypothesis Testing in Linear Models. 2nd Ed. Springer-Verlag, Berlin-Heidelberg, New York.
  • Yetkin, M. & Berber, M. (2013). Application of the sign-constrained robust least-squares method to surveying networks. Journal of Surveying Engineering, 139:1, 59-65. http://doi.org/10.1061/ (ASCE)SU.1943-5428.0000088
  • Fabozzi, F. J., Focardi, S. M., Rachev, S. T. & Arshanapalli, B. G. (2014). The Basics of Financial Econometric: Tools, Concepts and Asset Management Applications. John Wiley ve Sons, Inc.
  • Rousseeuw, P. J. & Hubert, M. (2018). Anomaly detection by robust statistics. Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery, 8:2, e1236. http://doi.org/10.1002/widm.1236
  • Bektas, S. & Sisman, Y. (2010). The comparison of L1 and L2-norm minimization methods. International Journal of the Physical Sciences, 5:11, 1721-1727. http://doi.org/10.5897/IJPS
  • Erdogan, B. (2014). An outlier detection method in geodetic networks based on the original observation. Boletim de Ciencias Geodesicas, 20:3, 578-589, http://doi.org/10.1590/S1982-2170201400030003 3
  • Giloni, A. & Padberg, M. (2001). Least Trimmed Squares Regression, Least Median Squares Regression and Mathematical Programming. Matmetical and Computer Modelling, 35:9-10, 1043-1060. http://doi.org/10.1016/S0895-7177(02)00069-9
  • Gui, Q. & Zhang, J. (1998). Robust biased estimation and its applications in geodetic adjustments. Journal of Geodesy, 72:7-8, 430-435. http://doi.org/10.1007/s00190005 0182
  • Hekimoglu, S. & Erenoglu, C. (2007). Jeodezik Ağlarda Uyuşumsuz Ölçülerin Klasik Yaklaşım ve Robust Yöntemlerle Belirlenmesi. Jeodezi ve Jeoinformasyon Dergisi, 97, 3-14.
  • Hubert, M., Rousseeuw, P. J. & Van Aelst, S. (2008). High-breakdown robust multivariate methods. Statistical science, 23:1, 92-119. http://doi.org/10.1214/088342307000000087
  • İnal, C. & Yetkin, M. (2006). Robust yöntemlerle uyuşumsuz ölçülerin belirlenmesi. Selçuk Üniversitesi Mühendisler-Mimarlar Fakültesi Dergisi, 21, 3-4.
  • Knight, N. L. & Wang, J. (2009). A comparison of outlier detection procedures and robust estimation methods in GPS positioning. The Journal of Navigation, 62:4, 699-709 http://doi.org/10.1017/S0373463309990142
  • Sisman, Y. (2010). Outlier measurements analysis with the robust estimation. Scientific Research and Essays, 5:6, 668-678.
  • Sisman, Y. (2011). Parameter estimation and outlier detection with different estimation methods. Scientific Research and Essays, 6:7, 1620-1626 http://doi.org/10.5897/SRE10.1181.
  • Susanti, Y., Pratiwi, H., Sulistijowati, S., & Liana, T. (2014). M estimation, S estimation, and MM estimation in robust regression. International Journal of Pure and Applied Mathematics, 91:3, 349-360. http://doi.org/10.12732/jipam. v91i3.7
  • Valero, J. L. B., & Moreno, S. B. (2005). Robust estimation in geodetic networks. Física de la Tierra, 17, 7.
  • Yang, Y. (1999). Robust estimation of geodetic datum transformation. Journal of Geodesy, 73:5, 268-274. http://doi.org/10.1007/s001900050243
  • Yetkin, M. & Inal, C. (2011). L1 norm minimization in GPS networks. Survey Review, 43:323, 523-532. http://doi.org/10.1179003962611x131177 48892038
  • Ogundare, J. O. (2018). Understanding Least Squares Estimation and Geomatics Data Analysis. John Wiley ve Sons, Inc, 111 River Street, Hoboken, NJ 07030, USA
  • Sisman, Y. & Bektas, S. (2012). Linear regression methods according to objective functions. Acta Montanistica Slovaca, 17:3, 209-217.
  • Grafarend, E. W. & Sansò, F. (Editors) (2012). Optimization and design of geodetic networks. Springer Science & Business Media, Heidelberg, Berlin.
  • Schaffrin, B. (2019). Notes on Adjustment Computations Part I.
  • Wells, D., & Krakiwsky, E. (1971). The Method of least squares. University of New Brunswick: Canada
  • Muhlbauer, A., Spichtinger, P., & Lohmann, U. (2009). Application and comparison of robust linear regression methods for trend estimation. Journal of Applied Meteorology and Climatology, 48:9, 1961-1970. http://doi.org/10.1175/2009JAMC1851.1
  • Hekimoğlu, Ş., Erdogan, B., Soycan, M., & Durdag, U. M. (2014). Univariate Approach for Detecting Outliers in Geodetic Networks. Journals of Surveying Engineering, 140:2, 04014006, 1-8. http://doi.org/10.1061/(ASCE)SU.19435428.0000123
  • Kavouras, M. (1982). On the detection of outliers and the determination of reliability in geodetic networks. Department of Surveying Engineering Technical Report No. 87, University of New Brunswick, Fredericton, N.B., November.
  • Sisman, Y. (2005). Uyuşumsuz Ölçü Gruplarının Belirlenmesi Yöntemleri. Harita Dergisi, 133.
  • Rousseeuw, J. R. (1990). Robust estimation and identifying outliers. Handbook of statistical methods for engineers and scientists, 16-1.
  • Huber, P. J. (1981). Robust Statistics. John Wiley and Sons, Inc.
  • Hofmann, M., Gatu, C., & Kontoghiorghes, E. J. (2010). An Exact Least Trimmed Squares Algorithm for a Range of Coverage Values, Journal of Computational and Graphical Statistics, 19:1, 191-204, http://doi.org/10.1198/jcgs.2009.07091
  • Rousseeuw, P. J. (1984). Least Median of Squares Regression. Joırnal of the American Statistical Association, 79:388, 871-880. http://doi.org/10.1080/016 21459.1984.10477105
  • Toka, O., & Cetin, M. (2011). The comparing of S-estimator and M-estimators in linear regression. Gazi University Journal of Science, 24, 4, 747-752
  • Staudte, R. G., & Sheather, S. J. (2011). Robust estimation and testing. John Wiley ve Sons, Inc, 918.
  • Cizek P (2005). Least trimmed squares in nonlinear regression under dependence. Journal of Statistical Planning, 136, 3967-3988, http://doi.org/10.1016/j.jspi.2005.05.004
  • Cizek, P., & Visek, J. A. (2000): Least trimmed squares, SFB 373 Discussion Paper, No. 2000, 53, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes, Berlin.
  • Rousseeuw, P. J., & Van Driessen, K. (2006). Computing LTS Regression for Large Data Sets. Data Min Knowl Disc 12, 29-45. https:/doi.org/10.1007/s10618-005-0024-4

New approaches for outlier detection: The least trimmed squares adjustment

Year 2023, Volume: 8 Issue: 1, 26 - 31, 15.02.2023

Hasan Dilmaç , Yasemin Şişman

https://doi.org/10.26833/ijeg.996340

Abstract

Classical outlier tests based on the least-squares (LS) have significant disadvantages in some situations. The adjustment computation and classical outlier tests deteriorate when observations include outliers. The robust techniques that are not sensitive to outliers have been developed to detect the outliers. Several methods use robust techniques such as M-estimators, L1- norm, the least trimmed squares etc. The least trimmed squares (LTS) among them have a high-breakdown point. After the theoretical explanation, the adjustment computation has been carried out in this study based on the least squares (LS) and the least trimmed squares (LTS). A certain polynomial with arbitrary values has been used for applications. In this way, the performances of these techniques have been investigated.

Keywords

The Least Squares Outliers Robust Estimation The Least Trimmed Squares

References

  • Fan, H. (1997). Theory of errors and least squares adjusment. Royal Instıtute of Technology, 72, 100-44, Stockholm, Sweden.
  • Ingram, E. L. (1911). Geodetic surveying and the adjustment of observations (methods of least squares). McGraw-Hill Book Company, Inc. 370 Seventh Avenue, New York.
  • Ghilani, C. D. (2017). Adjustment computations: Spatial data analysis (Sixth edition). John Wiley ve Sons, Inc., Hoboken, New Jersey.
  • Mikhail, E. M. & Ackermann, F. E. (1976). Observations and least squares. Thomas Y. Crowell Company, Inc. 666 Fifth Avenue, New York.
  • Čížek, P. & Víšek, J. Á. (2005). Least Trimmed Squares. XploRe®—Application Guide,49-63. Springer, Berlin, Heidelberg.doi: 10.1007/978-3-642-57292-0_2
  • Rousseeuw, J. R. & Leroy, A. M. (1987). Robust Regression and Outlier Detection. John Wiley ve Sons, Inc.
  • Hekimoglu, S. (2005). Do Robust Methods Identify Outliniers More Reliably Than Conventional Tests for Outliniers? Zeitschrift für Vermessungwesen, 3, 174-180.
  • Baarda, W. (1968). A testing procedure for use in geodetic networks. Netherlands Geodetic Com., New Series, Delft, Netherlands, 2(5).
  • Pope, A. J. (1976). The statistics of residuals and the detection of outliers. NOAA Technical Report. NOS 65 NGS 1, U. S. Dept. of Commerce, Rockville, Md.
  • Koch, K. R. (1999). Parameter Estimation and Hypothesis Testing in Linear Models. 2nd Ed. Springer-Verlag, Berlin-Heidelberg, New York.
  • Yetkin, M. & Berber, M. (2013). Application of the sign-constrained robust least-squares method to surveying networks. Journal of Surveying Engineering, 139:1, 59-65. http://doi.org/10.1061/ (ASCE)SU.1943-5428.0000088
  • Fabozzi, F. J., Focardi, S. M., Rachev, S. T. & Arshanapalli, B. G. (2014). The Basics of Financial Econometric: Tools, Concepts and Asset Management Applications. John Wiley ve Sons, Inc.
  • Rousseeuw, P. J. & Hubert, M. (2018). Anomaly detection by robust statistics. Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery, 8:2, e1236. http://doi.org/10.1002/widm.1236
  • Bektas, S. & Sisman, Y. (2010). The comparison of L1 and L2-norm minimization methods. International Journal of the Physical Sciences, 5:11, 1721-1727. http://doi.org/10.5897/IJPS
  • Erdogan, B. (2014). An outlier detection method in geodetic networks based on the original observation. Boletim de Ciencias Geodesicas, 20:3, 578-589, http://doi.org/10.1590/S1982-2170201400030003 3
  • Giloni, A. & Padberg, M. (2001). Least Trimmed Squares Regression, Least Median Squares Regression and Mathematical Programming. Matmetical and Computer Modelling, 35:9-10, 1043-1060. http://doi.org/10.1016/S0895-7177(02)00069-9
  • Gui, Q. & Zhang, J. (1998). Robust biased estimation and its applications in geodetic adjustments. Journal of Geodesy, 72:7-8, 430-435. http://doi.org/10.1007/s00190005 0182
  • Hekimoglu, S. & Erenoglu, C. (2007). Jeodezik Ağlarda Uyuşumsuz Ölçülerin Klasik Yaklaşım ve Robust Yöntemlerle Belirlenmesi. Jeodezi ve Jeoinformasyon Dergisi, 97, 3-14.
  • Hubert, M., Rousseeuw, P. J. & Van Aelst, S. (2008). High-breakdown robust multivariate methods. Statistical science, 23:1, 92-119. http://doi.org/10.1214/088342307000000087
  • İnal, C. & Yetkin, M. (2006). Robust yöntemlerle uyuşumsuz ölçülerin belirlenmesi. Selçuk Üniversitesi Mühendisler-Mimarlar Fakültesi Dergisi, 21, 3-4.
  • Knight, N. L. & Wang, J. (2009). A comparison of outlier detection procedures and robust estimation methods in GPS positioning. The Journal of Navigation, 62:4, 699-709 http://doi.org/10.1017/S0373463309990142
  • Sisman, Y. (2010). Outlier measurements analysis with the robust estimation. Scientific Research and Essays, 5:6, 668-678.
  • Sisman, Y. (2011). Parameter estimation and outlier detection with different estimation methods. Scientific Research and Essays, 6:7, 1620-1626 http://doi.org/10.5897/SRE10.1181.
  • Susanti, Y., Pratiwi, H., Sulistijowati, S., & Liana, T. (2014). M estimation, S estimation, and MM estimation in robust regression. International Journal of Pure and Applied Mathematics, 91:3, 349-360. http://doi.org/10.12732/jipam. v91i3.7
  • Valero, J. L. B., & Moreno, S. B. (2005). Robust estimation in geodetic networks. Física de la Tierra, 17, 7.
  • Yang, Y. (1999). Robust estimation of geodetic datum transformation. Journal of Geodesy, 73:5, 268-274. http://doi.org/10.1007/s001900050243
  • Yetkin, M. & Inal, C. (2011). L1 norm minimization in GPS networks. Survey Review, 43:323, 523-532. http://doi.org/10.1179003962611x131177 48892038
  • Ogundare, J. O. (2018). Understanding Least Squares Estimation and Geomatics Data Analysis. John Wiley ve Sons, Inc, 111 River Street, Hoboken, NJ 07030, USA
  • Sisman, Y. & Bektas, S. (2012). Linear regression methods according to objective functions. Acta Montanistica Slovaca, 17:3, 209-217.
  • Grafarend, E. W. & Sansò, F. (Editors) (2012). Optimization and design of geodetic networks. Springer Science & Business Media, Heidelberg, Berlin.
  • Schaffrin, B. (2019). Notes on Adjustment Computations Part I.
  • Wells, D., & Krakiwsky, E. (1971). The Method of least squares. University of New Brunswick: Canada
  • Muhlbauer, A., Spichtinger, P., & Lohmann, U. (2009). Application and comparison of robust linear regression methods for trend estimation. Journal of Applied Meteorology and Climatology, 48:9, 1961-1970. http://doi.org/10.1175/2009JAMC1851.1
  • Hekimoğlu, Ş., Erdogan, B., Soycan, M., & Durdag, U. M. (2014). Univariate Approach for Detecting Outliers in Geodetic Networks. Journals of Surveying Engineering, 140:2, 04014006, 1-8. http://doi.org/10.1061/(ASCE)SU.19435428.0000123
  • Kavouras, M. (1982). On the detection of outliers and the determination of reliability in geodetic networks. Department of Surveying Engineering Technical Report No. 87, University of New Brunswick, Fredericton, N.B., November.
  • Sisman, Y. (2005). Uyuşumsuz Ölçü Gruplarının Belirlenmesi Yöntemleri. Harita Dergisi, 133.
  • Rousseeuw, J. R. (1990). Robust estimation and identifying outliers. Handbook of statistical methods for engineers and scientists, 16-1.
  • Huber, P. J. (1981). Robust Statistics. John Wiley and Sons, Inc.
  • Hofmann, M., Gatu, C., & Kontoghiorghes, E. J. (2010). An Exact Least Trimmed Squares Algorithm for a Range of Coverage Values, Journal of Computational and Graphical Statistics, 19:1, 191-204, http://doi.org/10.1198/jcgs.2009.07091
  • Rousseeuw, P. J. (1984). Least Median of Squares Regression. Joırnal of the American Statistical Association, 79:388, 871-880. http://doi.org/10.1080/016 21459.1984.10477105
  • Toka, O., & Cetin, M. (2011). The comparing of S-estimator and M-estimators in linear regression. Gazi University Journal of Science, 24, 4, 747-752
  • Staudte, R. G., & Sheather, S. J. (2011). Robust estimation and testing. John Wiley ve Sons, Inc, 918.
  • Cizek P (2005). Least trimmed squares in nonlinear regression under dependence. Journal of Statistical Planning, 136, 3967-3988, http://doi.org/10.1016/j.jspi.2005.05.004
  • Cizek, P., & Visek, J. A. (2000): Least trimmed squares, SFB 373 Discussion Paper, No. 2000, 53, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes, Berlin.
  • Rousseeuw, P. J., & Van Driessen, K. (2006). Computing LTS Regression for Large Data Sets. Data Min Knowl Disc 12, 29-45. https:/doi.org/10.1007/s10618-005-0024-4
There are 45 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Hasan Dilmaç 0000-0001-6877-8730

Yasemin Şişman 0000-0002-6600-0623

Publication Date February 15, 2023
Published in Issue Year 2023 Volume: 8 Issue: 1

Cite

APA Dilmaç, H., & Şişman, Y. (2023). New approaches for outlier detection: The least trimmed squares adjustment. International Journal of Engineering and Geosciences, 8(1), 26-31. https://doi.org/10.26833/ijeg.996340
AMA Dilmaç H, Şişman Y. New approaches for outlier detection: The least trimmed squares adjustment. IJEG. February 2023;8(1):26-31. doi:10.26833/ijeg.996340
Chicago Dilmaç, Hasan, and Yasemin Şişman. “New Approaches for Outlier Detection: The Least Trimmed Squares Adjustment”. International Journal of Engineering and Geosciences 8, no. 1 (February 2023): 26-31. https://doi.org/10.26833/ijeg.996340.
EndNote Dilmaç H, Şişman Y (February 1, 2023) New approaches for outlier detection: The least trimmed squares adjustment. International Journal of Engineering and Geosciences 8 1 26–31.
IEEE H. Dilmaç and Y. Şişman, “New approaches for outlier detection: The least trimmed squares adjustment”, IJEG, vol. 8, no. 1, pp. 26–31, 2023, doi: 10.26833/ijeg.996340.
ISNAD Dilmaç, Hasan - Şişman, Yasemin. “New Approaches for Outlier Detection: The Least Trimmed Squares Adjustment”. International Journal of Engineering and Geosciences 8/1 (February 2023), 26-31. https://doi.org/10.26833/ijeg.996340.
JAMA Dilmaç H, Şişman Y. New approaches for outlier detection: The least trimmed squares adjustment. IJEG. 2023;8:26–31.
MLA Dilmaç, Hasan and Yasemin Şişman. “New Approaches for Outlier Detection: The Least Trimmed Squares Adjustment”. International Journal of Engineering and Geosciences, vol. 8, no. 1, 2023, pp. 26-31, doi:10.26833/ijeg.996340.
Vancouver Dilmaç H, Şişman Y. New approaches for outlier detection: The least trimmed squares adjustment. IJEG. 2023;8(1):26-31.