针对零膨胀模型的Score检验及其在自然灾害分析中的应用

摘要

To account for excess zeros relative to common Poisson distribution which are often encountered in natural science and society study, a class of zero-inflation Poisson mixed regression models is proposed. Nowadays, these models have been widely used in biology medical, insurance and other fields. And it is indispensable for testing whether there is zero-inflation exist in count data for models choosing. A score test is proposed for assessing zero-inflation in count data, and the sampling distribution and power of the score test statistic are also investigated by simulation studies. If there is zero-inflation exist, a data augmentation technique and Gibbs sampler are used to get the total parameter estimate. At last this test is further illustrated by a example about brushfire.%为了解释计数数据相对于普通的泊松分布存在过分多零的问题,一类零膨胀泊松混合回归模型被提出来.目前,该类模型已被广泛应用于生物医学、金融保险等研究领域中.而针对计数数据是否存在零膨胀的检验对于模型的选择是至关重要的.针对零膨胀是否存在的问题,提出了一种Score检验方法,并通过模拟研究考察了其检验统计量在原假设下的抽样分布与经验势,验证了该检验方法的可靠性.在零膨胀存在的情况下,结合数据分解技巧与Gibbs抽样方法对所有参数进行了估计.最后,利用一个关于森林火灾的实例对以上方法进行了进一步说明.