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Improved two-parameter estimators for the negative binomial and Poisson regression models

机译:负二项式和Poisson回归模型的改进的两参数估计量

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Negative binomial regression (NBR) and Poisson regression (PR) applications have become very popular in the analysis of count data in recent years. However, if there is a high degree of relationship between the independent variables, the problem of multicollinearity arises in these models. We introduce new two-parameter estimators (TPEs) for the NBR and the PR models by unifying the two-parameter estimator (TPE) of ozkale and Kaciranlar [The restricted and unrestricted two-parameter estimators. Commun Stat Theory Methods. 2007;36:2707-2725]. These new estimators are general estimators which include maximum likelihood (ML) estimator, ridge estimator (RE), Liu estimator (LE) and contraction estimator (CE) as special cases. Furthermore, biasing parameters of these estimators are given and a Monte Carlo simulation is done to evaluate the performance of these estimators using mean square error (MSE) criterion. The benefits of the new TPEs are also illustrated in an empirical application. The results show that the new proposed TPEs for the NBR and the PR models are better than the ML estimator, the RE and the LE.
机译:近年来,负二项式回归(NBR)和泊松回归(PR)应用在计数数据分析中非常流行。但是,如果自变量之间存在高度关联,则在这些模型中会出现多重共线性问题。通过统一ozkale和Kaciranlar的两参数估计量(TPE)[限制和无限制的两参数估计量,我们为NBR和PR模型引入了新的两参数估计量(TPE)。公共统计理论方法。 2007; 36:2707-2725]。这些新的估计器是一般估计器,其中包括最大似然(ML)估计器,岭估计器(RE),Liu估计器(LE)和收缩估计器(CE)作为特例。此外,给出了这些估计器的偏置参数,并进行了蒙特卡罗模拟,以使用均方误差(MSE)准则评估这些估计器的性能。新型TPE的优势也在经验应用中得到了说明。结果表明,针对NBR和PR模型新提议的TPE比ML估计器,RE和LE更好。

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