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ON SOME NEW RIDGE M-ESTIMATORS FOR LINEAR REGRESSION MODELS UNDER VARIOUS ERROR DISTRIBUTIONS.
- Source :
-
Pakistan Journal of Statistics . Oct2021, Vol. 37 Issue 4, p369-391. 23p. - Publication Year :
- 2021
-
Abstract
- Ridge regression is used to circumvent the problem of multicollinearity in the multiple linear regression models. Beside the multicollinearity, when the outliers in the y-direction are also present, then the usual ridge regression estimators gives inefficient results in terms of mean squared error (MSE). In order to mitigate such situation, ridge M-estimators are often used. Several estimators are available in literature but they do not perform well in terms of MSE when the joint problem of high multicollinearity and y-direction outliers is present. In this article, some new quantile based ridge M-estimators are proposed. The new estimators are then compared with other existing estimators through extensive Monte Carlo simulations for various error term distributions, degrees of multicollinearity and percentage of y-direction outliers. Based on simulation study with minimum MSE criterion, the new estimators outperform in many considered scenarios. Particularly, in case of high multicollinearity, y-direction outliers and heavy tailed error distributions, the proposed estimators have shown efficient results. A numerical example is also presented to support the simulation results. [ABSTRACT FROM AUTHOR]
- Subjects :
- *MULTICOLLINEARITY
*MONTE Carlo method
*REGRESSION analysis
Subjects
Details
- Language :
- English
- ISSN :
- 10129367
- Volume :
- 37
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Pakistan Journal of Statistics
- Publication Type :
- Academic Journal
- Accession number :
- 151577931