A new Poisson Liu Regression Estimator: method and application

Abstract

This paper considers the estimation of parameters for the Poisson regression model in the presence of high, but imperfect multicollinearity. To mitigate this problem, we suggest using the Poisson Liu Regression Estimator (PLRE) and propose some new approaches to estimate this shrinkage parameter. The small sample statistical properties of these estimators are systematically scrutinized using Monte Carlo simulations. To evaluate the performance of these estimators, we assess the Mean Square Errors (MSE) and the Mean Absolute Percentage Errors (MAPE). The simulation results clearly illustrate the benefit of the methods of estimating these types of shrinkage parameters in finite samples. Finally, we illustrate the empirical relevance of our newly proposed methods using an empirically relevant application. Thus, in summary, via simulations of empirically relevant parameter values, and by a standard empirical application, it is clearly demonstrated that our technique exhibits more precise estimators, compared to traditional techniques-at least when multicollinearity exist among the regressors.

A new estimator for the multicollinear Poisson regression model: simulation and application

“…Multicollinearity effects include significant variance and covariances of the regression coefficients, wider confidence intervals, insignificant t -ratios and high R-square. Multicollinearity also negatively influence the performance of the MLE in PRM 3 , 4 . Alternative estimators to the MLE in LRM are the ridge regression estimator by Hoerl and Kennard 5 , Liu estimator by Liu 6 , Liu type estimator by Liu 7 , two-parameter estimator by Ozkale and Kaciranlar 8 , k - d class estimator by Sakallioglu and Kaciranlar 9 , a two-parameter estimator by Yang and Chang 10 , modified two-parameter estimator by Dorugade 11 and recently, the modified ridge type estimator by Lukman et al 12 , modified new two-parameter estimator by Lukman et al 13 , modified new two-parameter estimator by Ahmad and Aslam 14 , and K–L estimator by Kibria and Lukman 15 .…”

“…Rashad and Algamal 20 developed a new ridge estimator for the Poisson regression model by modifying Poisson modified jackknifed ridge regression. Qasim et al 4 suggest some new shrinkage estimators for the PLE. We classified these estimators into Poisson regression estimators with a single shrinkage parameter and two-parameters, respectively.…”

“…To illustrate the finding of the paper, aircraft damage data was analyzed in Sect. 4. Some concluding remarks are presented in Sect.…”

New ridge estimators in the inverse Gaussian regression: Monte Carlo simulation and application to chemical data

“…The MLE may be unstable with wrong signs of the coefficients and the variances of the coefficients become inflated in the presence of multicollinearity. In addition, the interpretation of the estimated coefficients also becomes difficult (Qasim et al 2019;Amin, Akram, and Amanullah 2020). To resolve the issue of multicollinearity, many alternative biased estimation methods are provided in the literature.…”

Biased Adjusted Poisson Ridge Estimators-Method and Application

“…Algamal and Alanaz ( 2018 ) proposed different methods to estimate the value of ridge parameter ( k ) for PRRE. Rashad and Algamal ( 2019 ) proposed a new ridge regression approach in the PRM to reduce the issue of collinearity between explanatory variables, and recently Qasim et al ( 2019 ) proposed a Liu-type of regression estimator for the PRM. Türkan and Özel ( 2016 ) did not discuss the MSE properties of AUPRRE and MAUPRRE and not derive the optimal value of the ridge parameter ( k ).…”