In the last few years, diabetes mellitus and obesity revealed to be one of the fastest-growing chronic diseases in youth in the United States. The number of new diabetes cases is dramatically increasing, and, for the moment, effective therapy does not exist. Experts believe that one of the causes of this increase is the decline in exercise behavior. The California Education Code requires local educational agencies (LEAs) to administer the FITNESSGRAM, the Physical Fitness Test (PFT), to Californian students of public schools. This test evaluates six fitness areas, and experts defined that a passing result on all six areas of the test represents a fitness level that offers some protection against the diseases associated with physical inactivity. We consider 2015–2016 data provided by the California Department of Education (CDE): for each Californian county (), we aim at estimating the county-level proportion of students with a score equal to six. To account for the heterogeneity of the phenomenon and the presence of outlying counties, we extend the standard area-level model by specifying the random effects as a symmetric -stable (SS) distribution that can accommodate different types of outlying observations. The model can accurately estimate the county-level proportion of students with a score equal to six. Results highlight some interesting relationships with social and economic situations in each county. The performance of the proposed model is also investigated through an extensive simulation study.

中文翻译：

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一种新的鲁棒贝叶斯小区域估计，通过 - 稳定模型估计加州体育学生的比例

在过去几年中，糖尿病和肥胖症已成为美国青少年中增长最快的慢性病之一。新发糖尿病病例的数量正在急剧增加，目前尚不存在有效的治疗方法。专家认为，造成这种增加的原因之一是运动行为的下降。加州教育法规要求当地教育机构 (LEA) 为加州公立学校的学生管理 FITNESSGRAM，即体能测试 (PFT)。该测试评估六个健身领域，专家定义，测试的所有六个领域的通过结果代表一个健身水平，可以提供一定程度的保护，防止与缺乏身体活动相关的疾病。我们考虑了加州教育部 (CDE) 提供的 2015-2016 年数据：)，我们的目标是估计县级学生的分数等于 6 的比例。为了解释现象的异质性和外围县的存在，我们通过将随机效应指定为对称稳定(SS ) 分布来扩展标准区域级模型，该分布可以适应不同类型的外围观察。该模型可以准确估计县级分数等于 6 的学生比例。结果突出了每个县与社会和经济状况的一些有趣关系。所提出的模型的性能也通过广泛的模拟研究进行了调查。