ESTIMATE THE PARAMETERS IN PRESENCE OF MULTICOLLINEARITY AND OUTLIERS USING BISQUARE WEIGHTED RIDGE LEAST MEDIAN SQUARES REGRESSION (WRLMS)

  • KAFI DANO PATI College of Science, University of Duhok, Duhok, Kurdistan Region, Iraq –Dept Of Computer Science, College of Science, University of Duhok, Kurdistan Region–Iraq
Keywords: Multicollinearity; Outliers; Ridge Regression; Robust LMS Estimation and Weighted Ridge Least Median Squares.

Abstract

The presence of multicollinearity and outliers are classical problems of data within the linear
regression framework. We are going to present a proposal of a new method which can be a potential
candidate for robust ridge regression as well as a robust detection of multicollinearity. This proposal
arises as a logical combination of principles used in the ridge regression and the Bisquare weighted
function. The technique of the Least Median of Squares (LMS) is used for the sake of overcoming the
resulting regression problems. This paper investigates the non-resistance of Ordinary Least Square (OLS)
to multicollinearity and outliers and proposes the utilization of robust regression for instance, Least
Median Squares LMS to detect non-normality of residuals, the use of robust methods yields more reliable
trend estimations and outlier detection. LMS is introduced as a robust regression technique and through
medical application its effect on regression is discussed. The numerical example and simulation study
shows that the outcome of the Weighted Ridge Least Median Squares (WRLMS) is better than other
estimators in terms of its efficiency. This has been done by utilizing both Standard Error (SE) and the
Root Mean Squared Error criterion for the numerical example and simulation study, respectively as far
as a lot of combinations of error distribution and degree of multicollinearity are concerned.

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Published
2020-12-09
How to Cite
PATI, K. D. (2020). ESTIMATE THE PARAMETERS IN PRESENCE OF MULTICOLLINEARITY AND OUTLIERS USING BISQUARE WEIGHTED RIDGE LEAST MEDIAN SQUARES REGRESSION (WRLMS). Journal of Duhok University, 23(2), 9-24. https://doi.org/10.26682/sjuod.2020.23.2.2
Section
Pure and Engineering Sciences