On Comparison of Some Ridge Parameters in Ridge Regression

This study centers on estimating parameters in a linear regression model in the presence of multicollinearity. Multicollinearity poses a threat to the efficiency of the Ordinary Least Squares (OLS) estimator. Some alternative estimators have been developed as remedial measures to the earlier mentioned problem. This study introduces a new unbiased modified two-parameter estimator based on prior information. Its properties are also considered; the new estimator was compared with other estimators’ Mean Square Error (MSE). A numerical example and Monte Carlo simulation were used to illustrate the performance of the new estimator.

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“…Dorugade [5] introduced a Modified Two-Parameter (MTP) estimator, which was earlier defined in equation (7)…”

Section: The New Estimator and Its Propertiesmentioning

confidence: 99%

“…where 0 < d < 1. Dorugade [5] and Dorugade [6] introduced a modified two-parameter estimator. The estimator is given as:…”

Section: Introductionmentioning

confidence: 99%

Unbiased Modified Two-Parameter Estimator for the Linear Regression Model

et al. 2022

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“…Macedo [33] has improved the ridge-GME parameter estimator, which combines ridge regression and generalized maximum entropy to eliminate the subjectivity in the analysis of the ridge trace. Lukman et al [34] classify the estimators based on Dorugade [14] into different forms. They also provide some new ridge estimators.…”

Section: Literature Reviewmentioning

confidence: 99%

A Comparison of Different Ridge Parameters under Both Multicollinearity and Heteroscedasticity

Sevinç

Göktaş

2019

Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi

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One of the major problems in fitting an appropriate linear regression model is multicollinearity which occurs when regressors are highly correlated. To overcome this problem, ridge regression estimator which is an alternative method to the ordinary least squares (OLS) estimator, has been used. Heteroscedasticity, which violates the assumption of constant variances, is another major problem in regression estimation. To solve this violation problem, weighted least squares estimation is used to fit a more robust linear regression equation. However, when there is both multicollinearity and heteroscedasticity problem, weighted ridge regression estimation should be employed. Ridge regression depends on the ridge parameter which does not have an explicit form of calculation. There are various ridge parameters proposed in the literature. A simulation study was conducted to compare the performances of these ridge parameters for both multicollinear and heteroscedastic data. The following factors were varied: the number of regressors, sample sizes and degrees of multicollinearity. The performances of the parameters were compared using mean square error. The study also shows that when the data are both heteroscedastic and multicollinear, the estimation performances of the ridge parameters differs from the case for only multicollinear data.

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“…In the presence of collinearity problem, the well-know ridge regression estimators are proposed (Hoerl and Kennard, 1970). There are many studies in the literature that focus on ridge regression (Dorugade, 2014). Moreover, studies have suggested the use of robust and ridge-type robust estimators if there are outliers, or both collinearity and outliers, in the regression data (Aftab and Chand, 2018;Alshqaq, 2021;Maronna, 2011;Silvapulle, 1991).…”

Section: Introductionmentioning

confidence: 99%

An improved robust variance inflation factor: Reducing the negative effects of good leverage points

Ekiz

2021

KJS publishes peer-review articles in Mathematics, Computer Sci

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In multiple linear regression analysis, the variance inflation factor is a well-known collinearity measure. It is defined as the function of the coefficient of determination between the explanatory variables, and it is based on the maximum likelihood estimator of the regression coefficients. Nevertheless, in addition to outliers, leverage observations can have significant impact on the coefficient of determination, and thereby the variance inflation factor. This study presents an improved robust variance inflation factor estimator that is not affected by these observations. Simulation studies and a real data analysis indicate that the modified robust variance inflation factor estimator performs better than the traditional one.

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On Comparison of Some Ridge Parameters in Ridge Regression

Abstract: ABSTRACT

Cited by 9 publications

References 27 publications

Unbiased Modified Two-Parameter Estimator for the Linear Regression Model

Unbiased Modified Two-Parameter Estimator for the Linear Regression Model

A Comparison of Different Ridge Parameters under Both Multicollinearity and Heteroscedasticity

An improved robust variance inflation factor: Reducing the negative effects of good leverage points

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