A new approach called Weighted Least Squares Ratio (WLSR) Method to M-estimators

MURAT YAZICI

Abstract


Regression Analysis (RA) is an important statistical tool that is applied in most sciences. The Ordinary Least Squares (OLS) is a tradition method in RA and there are many regression techniques based on OLS. The Weighted Least Squares (WLS) method is iteratively used in M-estimators. The Least Squares Ratio (LSR) method in RA gives better results than OLS, especially in case of the presence of outliers. This paper includes a new approach to M-estimators, called Weighted Least Squares Ratio (WLSR), and comparison of WLS and WLSR according to mean absolute errors of estimation of the regression parameters (mae ß) and dependent value (mae y).


Keywords


Outliers; Least squares ratio (LSR) method; Weighted least squares ratio (WLSR) method; Robust statistics; M-estimators

Full Text:

PDF

References


Akbilgic O., Akinci E. D., 2009. A novel regression approach: Least squares ratio. Communications in Statistics - Theory and Methods, 38:9, 1539-1545,

Andersen R., 2007. Modern Methods for robust regression. Sage Publications.

Andrews D. F., 1974. A Robust method for multiple linear regression. Technometrics, Vol.16, 523-531.

Andrews D. F., Bickel P. J., Hampel F. R., Huber P. J., Rogers W. H., and Tukey J. W., 1972. Robust estimates of location. (Princeton Univ. Press, Princeton).

Banas M., Ligas M., 2014. Empirical tests of performance of some M – estimators. Geodesy and Cartography. Vol. 63, No 2, 2014, pp. 127-146

Chatterjee S., Machler M., 1997. Robust regression:a weighted least squares approach. Communications in Statistics - Theory and Methods, 26(6), 1381-1394.

Chang X.-W., Guo Y., 2005. Huber’s m-estimation in relative GPS positioning: computational aspects. Journal of Geodesy, Volume 79, Issue 6-7, pp 351-362.

Drapper N. R., Smith H., 1998. Applied regression analysis. New York: Wiley.

Duchnowski, R. 2011. Sensitivity of robust estimators applied in strategy for testing stability of reference points. EIF approach. Geodesy and Cartography, 60(2), 123-134

Hoaglin D. C, Mosteller F., and Tukey J. W., 1983. Understanding robust and exploratory data analysis. John Wiley and Sons, New York.

Huber P. J., 1964. Robust estimation of a location parameter. The Annals of Mathematical Statistics, 35(1), 73-101.

Koller M., Stahel W. A., 2011. Sharpening wald-type inference in robust regression for small samples. Computational Statistics & Data Analysis 55 (8), 2504–2515.

Muthukrishnan R., Radha M., 2010. M-estimators in regression models. Journal of Mathematics Research. Vol. 2, No. 4, pp. 23-27.

Rousseeuw P. J., Leroy A. M., 2003. Robust regression and outlier detection. Wiley-Interscience; first edition.


Refbacks

  • There are currently no refbacks.


Copyright (c) 2015 Journal of Information Sciences and Computing Technologies

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

 

Copyright © 2014 Journal of Information Sciences and Computing Technologies. All rights reserved.

ISSN: 2394-9066

For any help/support contact us at jiscteditor@scitecresearch.com.