THE JACKKNIFED BETA RIDGE REGRESSION ESTIMATOR: MATHEMATICAL PROGRAMMING APPROACH
Keywords:
ridge regression estimator, jackknifed ridge regression estimator, mathematical programming, beta regression, multicollinearityDOI:
https://doi.org/10.17654/0972361723007Abstract
For modelling proportions measured on a continuous scale, a nonlinear regression model is used, which is the beta regression model, and its parameters are estimated with the maximum likelihood method. It assumes that the explanatory variables are uncorrelated as in a linear regression model. If this is not the case, then multicollinearity shows biased estimators such as ridge regression and Liu-type, among others, are used for adjusting the multicollinearity problem. In this study, a jackknifed beta ridge regression estimator (JBRRE) is proposed, and its performance is theoretically assessed by the use of the matrix mean squared errors and the scalar mean squared errors. Additionally, a single-objective nonlinear model is suggested to determine the optimal value of the ridge shrinkage parameter. Also, the proposed biased estimator is applied to a real data set taken from the Egyptian Annual Bulletin of Health Services Statistics of the year 2018 (Treatment Facilities of the Egyptian Government Sector in 2018). The results show that the performance of the proposed biased estimator with the optimal shrinkage parameter using the suggested mathematical programming model outperforms other estimators.
Received: September 10, 2022; Revised: November 23, 2022; Accepted: December 22, 2022; Published: January 6, 2023
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