平方根变换下计数数据小面积估计的单位级模型

IF 0.6 4区 数学 Q4 STATISTICS & PROBABILITY
Kelly C. M. Gonçalves, M. Ghosh
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引用次数: 2

摘要

摘要近年来,世界范围内对小区域统计的需求大大增加。小区域模型是用随机的区域特定效应来制定的,假设它可以解释无法由辅助变量解释的区域间变化。单位水平模型将研究变量的单位值与单位特定协变量联系起来。本文的主要目的是考虑基于计数数据的单位级模型下的小面积估计。特别是,我们考虑原始数据的平方根变换,而不是假设泊松分布的变量建模,这是一种通常的选择。一个实际的优点是,所提出的变换实现了误差方差的近似同方差,减少了一层估计问题。模型的推理是在层次贝叶斯方法下进行的。在一个模拟研究和两个基于设计的实际数据集研究中,对平方根变换进行了评估。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Unit level model for small area estimation with count data under square root transformation
Abstract. In recent years, the demand for small area statistics has greatly increased worldwide. Small area models are formulated with random area-specific effects assumed to account for the between-area variation that is not explained by auxiliary variables. The unit level models relate the unit values of a study variable to unit-specific covariates. The main aim of this paper is to consider small area estimation under unit level models based on count data. In particular, instead of modelling the variables assuming the Poisson distribution, which is a usual choice, we consider the square root transformation of the original data. One practical advantage is that the proposed transformation achieves approximate homoscedasticity of the error variances, reducing one layer of estimation problem. Inference for the model is carried out under the hierarchical Bayes approach. The square root transformation is evaluated under a simulation study and two design-based studies with real datasets.
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来源期刊
CiteScore
1.60
自引率
10.00%
发文量
30
审稿时长
>12 weeks
期刊介绍: The Brazilian Journal of Probability and Statistics aims to publish high quality research papers in applied probability, applied statistics, computational statistics, mathematical statistics, probability theory and stochastic processes. More specifically, the following types of contributions will be considered: (i) Original articles dealing with methodological developments, comparison of competing techniques or their computational aspects. (ii) Original articles developing theoretical results. (iii) Articles that contain novel applications of existing methodologies to practical problems. For these papers the focus is in the importance and originality of the applied problem, as well as, applications of the best available methodologies to solve it. (iv) Survey articles containing a thorough coverage of topics of broad interest to probability and statistics. The journal will occasionally publish book reviews, invited papers and essays on the teaching of statistics.
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