Yang Zhihuang, Chen Jiahua
School of Mathematics and Statistics, Yunnan University, Kunming, People's Republic of China.
Department of Statistics, University of British Columbia, Vancouver, Canada.
J Appl Stat. 2019 Jul 30;47(4):602-623. doi: 10.1080/02664763.2019.1648390. eCollection 2020.
Providing reliable estimates of subpopulation/area parameters has attracted increased attention due to their importance in applications such as policymaking. Due to low or even no samples from some areas, we must adopt indirect model approaches. Existing indirect small area estimation methods often assume that a single nested error regression model is suitable for all the small areas. In particular, the effects of the auxiliary variables are either fixed or have a single attraction center. In some applications, it can be more appropriate to cluster the small areas so that the effects of the auxiliary variables are fixed but have multiple centers in the nested error regression model. In this paper, we examine an extended nested error regression model in which the auxiliary variables have mixed effects with multiple centers. We use a penalty approach to identify these centers and estimate the model parameters simultaneously. We then propose two new small area mean estimators and construct estimators of their mean square errors. Simulations based on artificial and realistic finite populations show that the new estimators can be efficient. Furthermore, the confidence intervals based on the new methods have accurate coverage probabilities. We illustrate the proposed methods with the Survey of Labour and Income Dynamics conducted in Canada.
由于在政策制定等应用中的重要性，提供亚群体/区域参数的可靠估计已引起越来越多的关注。由于某些地区的样本很少甚至没有样本，我们必须采用间接模型方法。现有的间接小区域估计方法通常假设单个嵌套误差回归模型适用于所有小区域。特别是，辅助变量的影响要么是固定的，要么有一个单一的吸引中心。在某些应用中，将小区域聚类可能更合适，这样在嵌套误差回归模型中辅助变量的影响是固定的但有多个中心。在本文中，我们研究了一种扩展的嵌套误差回归模型，其中辅助变量具有多个中心的混合效应。我们使用惩罚方法来识别这些中心并同时估计模型参数。然后我们提出了两个新的小区域均值估计量，并构造了它们的均方误差估计量。基于人工和现实有限总体的模拟表明，新的估计量可能是有效的。此外，基于新方法的置信区间具有准确的覆盖概率。我们用加拿大进行的劳动力和收入动态调查来说明所提出的方法。
