Classification-Based Ridge Estimation Techniques of Alkhamisi Methods (2025)

Review and Classifications of the Ridge Parameter Estimation Techniques

Hacettepe Journal of Mathematics and Statistics, 2016

Ridge parameter estimation techniques under the inuence of multicollinearity in Linear regression model were reviewed and classied into dierent forms and various types. The dierent forms are Fixed Maximum (FM), Varying Maximum (VM), Arithmetic Mean (AM), Geometric Mean (GM), Harmonic Mean (HM) and Median (M) and the various types are Original (O), Reciprocal (R), Square Root (SR) and Reciprocal of Square Root (RSR). These classications resulted into proposing some other techniques of Ridge parameter estimation. Investigation of the existing and proposed ones were done by conducting 1000 Monte-Carlo experiments under ve (5) levels of multicollinearity (ρ = 0.8, 0.9, 0.95, 0.99, 0.999), three (3) levels of error variance (σ 2 = 0.25, 1, 25) and ve levels of sample size (n = 10, 20, 30, 40, 50). The relative eciency (RF ≤ 0.75) of the techniques resulting from the ratio of their mean square error and that of the ordinary least square was used to compare the techniques. Results show that the proposed techniques perform better than the existing ones in some situations; and that the best technique is generally the ridge parameter in the form of Harmonic Mean, Fixed Maximum and Varying Maximum in their Original and Square Root types.

Review and classications of the ridge parameter estimation techniques

Hacettepe Journal of Mathematics and Statistics, 2017

Ridge parameter estimation techniques under the inuence of multicollinearity in Linear regression model were reviewed and classied into dierent forms and various types. The dierent forms are Fixed Maximum (FM), Varying Maximum (VM), Arithmetic Mean (AM), Geometric Mean (GM), Harmonic Mean (HM) and Median (M) and the various types are Original (O), Reciprocal (R), Square Root (SR) and Reciprocal of Square Root (RSR). These classications resulted into proposing some other techniques of Ridge parameter estimation. Investigation of the existing and proposed ones were done by conducting 1000 Monte-Carlo experiments under ve (5) levels of multicollinearity (ρ = 0.8, 0.9, 0.95, 0.99, 0.999), three (3) levels of error variance (σ 2 = 0.25, 1, 25) and ve levels of sample size (n = 10, 20, 30, 40, 50). The relative eciency (RF ≤ 0.75) of the techniques resulting from the ratio of their mean square error and that of the ordinary least square was used to compare the techniques. Results show that the proposed techniques perform better than the existing ones in some situations; and that the best technique is generally the ridge parameter in the form of Harmonic Mean, Fixed Maximum and Varying Maximum in their Original and Square Root types.

Monte Carlo study of some classification-based ridge parameter estimators

Journal of Modern Applied Statistical Methods

Ridge estimator in linear regression model requires a ridge parameter, K, of which many have been proposed. In this study, estimators based on Dorugade (2014) and Adnan et al. (2014) were classified into different forms and various types using the idea of Lukman and Ayinde (2015). Some new ridge estimators were proposed. Results shows that the proposed estimators based on Adnan et al. (2014) perform generally better than the existing ones.

A computer intensive method for choosing the ridge parameter

2004

A Comparative Study on the Performance of New Ridge Estimators

Pakistan Journal of Statistics and Operation Research, 2016

Least square estimators in multiple linear regressions under multicollinearity become unstable as they produce large variance for the estimated regression coefficients. Hoerl and Kennard 1970, developed ridge estimators for cases of high degree of collinearity. In ridge estimation, the estimation of ridge parameter (k) is vital. In this article new methods for estimating ridge parameter are introduced. The performance of the proposed estimators is investigated through mean square errors (MSE). Monte-Carlo simulation technique indicated that the proposed estimators perform better than ordinary least squares (OLS) estimators as well as few other ridge estimators.

Alternative Ridge Parameters in Linear Model

Nicel Bilimler Dergisi

The ridge regression estimator produces efficient estimates than the Ordinary Least Square Estimator in a linear regression model that has multicollinearity problem. However, the efficiency of the ridge estimator depends on the choice of the ridge parameter, k. This parameter being the biasing parameter that shrinks the coefficient as it tends towards positive infinity needs to be chosen optimally to minimize the mean squared errors of the parameters. In this study, the ridge parameters are classified into different forms, various types and diverse kinds. These classifications resulted into proposing some other techniques of Ridge parameter estimation. Investigation of the existing and proposed ridge parameters were done by conducting Monte-Carlo experiments. Results from simulation study and reallife data application show that some newly proposed ridge parameters are among those that provide efficient estimates.

On Comparison of Some Ridge Parameters in Ridge Regression

Sri Lankan Journal of Applied Statistics, 2014

In this article, a new approach to obtain the ridge parameter introduces for the multiple linear regression model suffers from the problem of multicollinearity. Furthermore, we compare the proposed ridge parameter with the other well-known ridge-parameters through ridge estimators evaluated elsewhere in terms of mean squares error (MSE) criterion. Finally, a numerical example and simulation study has been conducted to illustrate the optimality of the proposed ridge parameter.

Performance of the New Ridge Regression Parameters

Journal of Advances in Mathematics and Computer Science

A new approach is presented to find the ridge parameter k when the multiple regression model suffers from multicollinearity. This approach studied two cases, for the value k, scalar, and matrix. A comparison between this proposed ridge parameter and other well-known ridge parameters evaluated elsewhere, in terms of the mean squares error criterion, is given. Examples from several research papers are conducted to illustrate the optimality of this proposed ridge parameter k.

Some Improved Classification-Based Ridge Parameter of Hoerl and Kennard Estimation Techniques

West African Journal of Industrial and Academic Research, 2016

In a linear regression model, it is often assumed that the explanatory variables are independent. This assumption is often violated and Ridge Regression estimator introduced by [2]has been identified to be more efficient than ordinary least square (OLS) in handling it. However, it requires a ridge parameter, K, of which many have been proposed. In this study, estimators based on Hoerl and Kennard were classified into different forms and various types and some modifications were proposed to improveit. Investigation were done by conducting 1000 Monte-Carlo experiments under five (5) levels of multicollinearity, three (3) levels of error variance and five levels of sample size. For the purpose of comparing the performance of the improved ridge parameter with the existing ones, the number of times the MSE of the improved ridge parameter is less than the existing ones is counted over the levels of multicollinearity (5) and error variance (3). Also, a maximum of fifteen (15) counts is exp...

Modifying Two-Parameter Ridge Liu Estimator Based on Ridge Estimation

Pakistan Journal of Statistics and Operation Research, 2019

In this paper, we introduce the new biased estimator to deal with the problem of multicollinearity. This estimator is considered a modification of Two-Parameter Ridge-Liu estimator based on ridge estimation. Furthermore, the superiority of the new estimator than Ridge, Liu and Two-Parameter Ridge-Liu estimator were discussed. We used the mean squared error matrix (MSEM) criterion to verify the superiority of the new estimate. In addition to, we illustrated the performance of the new estimator at several factors through the simulation study.