Abstract
The multiple linear errors-in-variables model is frequently used in science and engineering for model fitting tasks. When sample data is contaminated by outliers, the orthogonal least squares estimator isn’t robust. To obtain robust estimators, orthogonal least trimmed absolute deviation (OLTAD) estimator based on the subset of h cases(out of n) is proposed. However, the OLTAD estimator is NP-hard to compute. So, an new decimal-decimal-integer-coded genetic algorithm(DICGA) for OLTAD estimator is presented. We show that the OLTAD estimator has the high breakdown point and appropriate properties. Computational experiments of the OLTAD estimator of multiple linear EIV model on synthetic data is provided and the results indicate that the DICGA performs well in identifying groups of high leverage outliers in reasonable computational time and can obtain smaller objective function fitness.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ruiz-Gazenb, A., Fekria, M.: Robust estimation in the simple errors-in-variables model. Statistics & Probability Letters 76(16), 1741–1747 (2006)
Zamar, R.H.: Robust estimation in the errors-in-variables model. Biometrika 76(1), 149–160 (1989)
Zamar, R.H.: Bias robust estimation in the orthogonal regression. The Annals of Statistics 20(4), 1875–1888 (1992)
Croux, C., Haesbroeck, G.: Principal component analysis based on robust estimators of the covariance or correlation matrix: influence functions and efficiencies. Biometrika 87(3), 603–618 (2000)
Fekri, M., Ruiz-Gazen, A.: Robust weighted orthogonal regression in the errors-in-variables model. Journal of Multiple Analysis 88(1), 89–108 (2004)
Jung, K.M.: Least trimmed squares estimator in the errors-in-variables model. Applied Statistics 34(3), 331–338 (2007)
Hu, T., Cui, H.J.: T-type estimators for a class of linear errors-in-variables models. Statistica Sinica 19, 1013–1036 (2009)
Nunkessera, R., Morell, O.: An evolutionary algorithm for robust regression. Computational Statistics & Data Analysis 54(12), 3242–3248 (2010)
Akter, S., Khan, M.H.A.: Multiple-case outlier detection in multiple linear regression model using quantum-inspired evolutionary algorithm. Journal of Computers 5(12), 1779–1788 (2010)
Croux, Fekri, M., Ruiz-Gazen, A.: Fast and robust estimation of the multivariate errors in variables model. Test 19(2), 286–303 (2010)
Rousseeuw, P.J., Leroy, A.M.: Robust Regression and Outliers Detection. John Wiley and Son (1987)
Cui, H.J.: Asymptotic properties of Generalized LAD estimators in EV model (in Chinese). Science in China (Series A) 27(2), 119–131 (1997)
Feng, S.P.: Optimal solution on weighted total least absolute deviation (in Chinese). Journal of University of Science and Technology of China 39(12), 1260–1264 (2009)
Forrest, S.: Genetic algorithms: Principles of natural selection applied to computation. Science 261(5123), 872–878 (1993)
Chatterjeea, S., Laudatoa, M., Lynchb, L.A.: Genetic algorithms and their statistical applications: an introduction. Computational Statistics and Data Analysis 22(6), 633–651 (1996)
Rousseeuw, P.J., Van Driessen, K.: Computing lts regression for large data sets. Data Mining and Knowledge Discovery 12(1), 29–45 (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wang, F., Cao, H., Qian, X. (2011). Decimal-Integer-Coded Genetic Algorithm for Trimmed Estimator of the Multiple Linear Errors in Variables Model. In: Liu, B., Chai, C. (eds) Information Computing and Applications. ICICA 2011. Lecture Notes in Computer Science, vol 7030. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25255-6_46
Download citation
DOI: https://doi.org/10.1007/978-3-642-25255-6_46
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-25254-9
Online ISBN: 978-3-642-25255-6
eBook Packages: Computer ScienceComputer Science (R0)