Abstract

In this paper, we address the estimation of fixed effects parameters in the zero-inflated negative binomial mixed model based on shrinkage estimators, namely linear shrinkage, pretest, shrinkage pretest, shrinkage, and positive-shrinkage estimators when the random effects are considered as nuisance parameters. We compare the performance of the shrinkage estimators to unrestricted and restricted estimators when certain prior subspace information is available. The asymptotic distributional biases and risks of the proposed estimators are obtained. We also conduct a Monte Carlo simulation study to compare the performance of each estimator in the sense of simulated relative efficiency. The results of simulation study show that the proposed estimation strategies perform strongly better than the maximum likelihood method. Finally, proposed methodologies are applied to a real dataset to appraise their performances.

摘要

在本文中，我们解决了基于收缩估计器的零膨胀负二项式混合模型中固定效应参数的估计，即线性收缩、预测试、收缩预测试、收缩和当随机效应被视为有害参数时的正收缩估计器。当某些先验子空间信息可用时，我们将收缩估计器的性能与无限制和受限估计器进行比较。获得了所提出的估计量的渐近分布偏差和风险。我们还进行了蒙特卡罗模拟研究，以在模拟相对效率的意义上比较每个估计器的性能。仿真研究的结果表明，所提出的估计策略的性能明显优于最大似然法。最后，