Abstract The Poisson regression model (PRM) is the standard statistical method of analyzing count data, and it is estimated by a Poisson maximum likelihood (PML) estimator. Such an estimator is affected by outliers, and some robust Poisson regression estimators have been proposed to solve this problem. PML estimators are also influenced by multicollinearity. Biased Poisson regression estimators have been developed to address this problem, including Poisson ridge regression and Poisson almost unbiased ridge estimators. However, the above mentioned estimators do not deal with outliers and multicollinearity problems together in a PRM. Therefore, we propose two robust ridge estimators to deal with the two problems simultaneously in the PRM, namely, the robust Poisson ridge regression (RPRR) estimator and the robust Poisson almost unbiased ridge (RPAUR) estimator. Theoretical comparisons and Monte‐Carlo simulations are conducted to investigate the performance of the proposed estimators relative to the performance of other approaches to PRM parameter estimation. The simulation results indicate that the RPAUR estimator outperforms the other estimators in all situations where both problems exist. Finally, real data are used to confirm the results of this paper.

Abstract The Zero‐inflated negative binomial (ZINB) regression models are mainly applied for count data that shows over‐dispersion and extra zeros. Multicollinearity is considered to be a significant problem in the estimation of parameters in the ZINB regression model. Thus, in order to alleviate the serious effects of multicollinearity, a new estimator is proposed which is called ZINB Stein estimator (ZINBSE). We also proposed various biasing parameters for the ZINBSE. A theoretical comparison is also conducted with some existing estimators in the literature. A Monte Carlo simulation study has been considered in order to judge the superiority of the proposed and other estimators, where the estimated mean squared error and mean absolute error are the evaluation criterion. An empirical application is also considered for illustration purposes. Based on the simulation and application results, it is observed that the new ZINBSE with proposed biasing parameters are superior over the other competitors' estimators.

Abstract The beta regression model is a commonly used when the response variable has the form of fractions or percentages. The maximum likelihood (ML) estimator is used to estimate the regression coefficients of this model. However, it is known that multicollinearity problem affects badly the variance of ML estimator. Therefore, this paper introduces the Liu‐type estimator for the beta regression model to handle the multicollinearity problem. The performance of the proposed (Liu‐type) estimator is compared to the ML estimator and other biased (ridge and Liu) estimators depending on the mean squared error (MSE) criterion by conducting a simulation study and through an empirical application. The results indicated that the proposed estimator outperformed the ML, ridge, and Liu estimators.

Abstract The ordinary least‐squares estimator is commonly used to estimate the parameters of a linear regression model but gives unreliable and unfavorable results when two problems occur together: multicollinearity and outliers. This article proposes two different robust estimators of the regression parameters to cope with these problems together. The proposed estimators are a robust version of the Özkale–Kaçiranlar and Yang–Chang estimators. Theoretical calculations, numerical simulations, and real‐life data on manufacturing production are presented to demonstrate the superiority of the proposed robust estimators to existing estimators at dealing with multicollinearity and outliers at the same time.