Title: On some beta ridge regression estimators: Methods, simulation and application
Authors: Muhammad Qasim - Jonkoping University (Sweden) [presenting]
Kristofer Mansson - JU JIBS (Sweden)
BM Golam Kibria - Department of Mathematics and Statistics Florida International University USA (United States)
Abstract: The classic statistical method for modelling the rates and proportions is the beta regression model (BRM). The BRM is applicable when the dependent variable is continuous, beta distributed and limited in the interval (0, 1). The standard maximum likelihood estimator (MLE) is used to estimate the coefficients of the BRM. However, this MLE is very sensitive when the regressors are linearly correlated to each other. Therefore, a new beta ridge regression (BRR) estimator is introduced as a remedy to the problem of instability of the MLE. We study the mean square error properties (MSE) of this estimator analytically, and then, based on the derived MSE, we suggest some new estimators of the shrinkage parameter. We also suggest a median square error (SE) performance criteria which can be used to achieve strong evidence in favor of proposed method for the Monte Carlo simulation study. The performance of BRR and MLE is appraised by means of Monte Carlo simulation where mean and median SE are used as performance criteria. We found that the proposed estimators performed better than some existing estimators. Finally, an empirical application is used to show the advantages of the proposed estimator.