Modified Ridge Regression Estimators

Khalaf, Ghadban; Månsson, Kristofer; Shukur, Ghazi

doi:10.1080/03610926.2011.593285

Cited by 49 publications

(14 citation statements)

References 8 publications

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“…By adopting the idea of Ref. [1], we multiply a quantity V Mj � λ j /|α Mj | with K as suggested by Ref. [8].…”

Section: New Estimatorsmentioning

confidence: 99%

“…e estimator β is unbiased and has minimum variance among all the linear unbiased estimators. However, the performance of this estimator is poor in the presence of multicollinearity, such that it is statistically insignificant with large variance [1]. To cope with this issue, several alternatives have been developed.…”

Section: Introduction E Matrix Form Of the Multiple Linear Regression Model Ismentioning

confidence: 99%

“…[8] and following the idea of Ref. [1], we proposed the modified ridge M-estimators in TPR. e developed M-estimators provide the minimum MSE than OLS, RR, and existing TPR estimators for different levels of correlation, sample size, error variance, and outliers.…”

Section: Introduction E Matrix Form Of the Multiple Linear Regression Model Ismentioning

confidence: 99%

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Modified Robust Ridge M-Estimators in Two-Parameter Ridge Regression Model

Yasin

Salem

Ayed

et al. 2021

Mathematical Problems in Engineering

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The methods of two-parameter ridge and ordinary ridge regression are very sensitive to the presence of the joint problem of multicollinearity and outliers in the y-direction. To overcome this problem, modified robust ridge M-estimators are proposed. The new estimators are then compared with the existing ones by means of extensive Monte Carlo simulations. According to mean squared error (MSE) criterion, the new estimators outperform the least square estimator, ridge regression estimator, and two-parameter ridge estimator in many considered scenarios. Two numerical examples are also presented to illustrate the simulation results.

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“…By adopting the idea of Ref. [1], we multiply a quantity V Mj � λ j /|α Mj | with K as suggested by Ref. [8].…”

Section: New Estimatorsmentioning

confidence: 99%

Section: Introduction E Matrix Form Of the Multiple Linear Regression Model Ismentioning

confidence: 99%

See 1 more Smart Citation

Modified Robust Ridge M-Estimators in Two-Parameter Ridge Regression Model

Yasin

Salem

Ayed

et al. 2021

Mathematical Problems in Engineering

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“…As the ridge estimator is heavily dependent on the unknown value of k, "the optimum value for k that can produce the best results to some extent is still an open problem in the literature. The estimatorβ k is a complicated function of k and several authors presented their proposals for the estimation of k [3]- [25].…”

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confidence: 99%

On the Performance of Jackknife Based Estimators for Ridge Regression

et al. 2021

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Regression techniques are generally used to predict a response variable using one or more predictor variables. In many fields of study, the regressors can be highly intercorrelated, which leads to the problem of multicollinearity. Consequently, the ordinary least squares estimates become inconsistent and lead to wrong inferences. To handle the problem, machine learning techniques particularly, the ridge regression approach, are commonly used. In this paper, we revisit the problem of estimating the ridge parameter "k" by proposing some new estimators using the Jackknife method and compare them with some existing estimators. The performance of the proposed estimators compared to the existing ones is evaluated using extensive Monte Carlo simulations as well as two real data sets. The results suggested that the proposed estimators outperform the existing estimators.

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“…[10] proposed methods for estimating the ridge parameter(s). [4] proposed different estimators of the ridge parameter k and compared ,via simulation, with estimators proposed by [6], [5], and [10].…”

Section: Introductionmentioning

confidence: 99%

New Approaches for Choosing the Ridge Parameters

Al-Jararha¹

2016

HJMS

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Consider the standard multiple linear regression model y = xβ +ε. If the correlation matrix x t x is ill-conditioned, the ordinary least squared estimate (ols)β of β is not the best choice. In this paper, multiple regularization parameters for different coefficients in ridge regression are proposed. The Mean Squared Error (MSE) of a ridge estimate based on the multiple regularization parameters is less than or equal to the MSE of the ridge estimate based on [2]. The proposed approach, depending on the condition numbers, leave's zero for the largest eigenvalue of x t x and gives the largest value for the smallest eigenvalue of x t x. Furthermore, if x t x is nearly a unit matrix, x t x is not an ill-conditioned one. The proposed approach gives approximately the same results as the ols estimates. The proposed approach can also be modified to give other new ridge parameters. The modified approach depends on the eigenvalues of x t x and differ from the ridge parameter proposed by [5] by a factor. The body fat data set has severe multicollinearity and is used to compare different approaches.Mathematical Subject Classification: Primary 62J02 Secondary 62J12

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Modified Ridge Regression Estimators

Cited by 49 publications

References 8 publications

Modified Robust Ridge M-Estimators in Two-Parameter Ridge Regression Model

Modified Robust Ridge M-Estimators in Two-Parameter Ridge Regression Model

On the Performance of Jackknife Based Estimators for Ridge Regression

New Approaches for Choosing the Ridge Parameters

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