RESUMO
The Poisson Regression Model (PRM) is one of the benchmark models when analyzing the count data. The Maximum Likelihood Estimator (MLE) is used to estimate the model parameters in PRMs. However, the MLE may suffer from various drawbacks that arise due to the existence of multicollinearity problems. Many estimators have been proposed as alternatives to each other to alleviate the multicollinearity problem in PRM, such as Poisson Ridge Estimator (PRE), Poisson Liu Estimator (PLE), Poisson Liu-type Estimator (PLTE), and Improvement Liu-Type Estimator (ILTE). In this study, we define a new general class of estimators which is based on the PRE as an alternative to other existing biased estimators in the PRMs. The superiority of the proposed biased estimator over the other existing biased estimators is given under the asymptotic matrix mean square error sense. Furthermore, two separate Monte Carlo simulation studies are implemented to compare the performances of the proposed biased estimators. Finally, the performances of all considered biased estimators are shown in real data.
RESUMO
In mixture experiments, estimation of the parameters is generally based on ordinary least squares (OLS). However, in the presence of multicollinearity and outliers, OLS can result in very poor estimates. In this case, effects due to the combined outlier-multicollinearity problem can be reduced to certain extent by using alternative approaches. One of these approaches is to use biased-robust regression techniques for the estimation of parameters. In this paper, we evaluate various ridge-type robust estimators in the cases where there are multicollinearity and outliers during the analysis of mixture experiments. Also, for selection of biasing parameter, we use fraction of design space plots for evaluating the effect of the ridge-type robust estimators with respect to the scaled mean squared error of prediction. The suggested graphical approach is illustrated on Hald cement data set.
