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Hierarchical Bayes estimation of small area means under a spatial nonstationary Fay–Herriot model
Communications in Statistics - Simulation and Computation ( IF 0.8 ) Pub Date : 2021-05-24 , DOI: 10.1080/03610918.2021.1926501
Priyanka Anjoy 1 , Hukum Chandra 1
Affiliation  

Abstract

The Fay–Herriot (FH) model is widely used in small area estimation (SAE) for aggregated level data, but in several applications presence of spatial effect between contiguous or neighboring region cannot be denied which is not handled by this model. Conditional Autoregressive and Simultaneous Autoregressive specifications do incorporate spatial associationship while taking into account the spatial correlation effects among areas. However, none of these approaches implement the idea of spatially varying covariates through spatially dependent fixed effect parameters. Such approach in statistics is known as spatial nonstationarity. This article introduces spatial nonstationary version of FH model considering hierarchical Bayesian paradigm and then deliberates estimation of small area means. The proposed SAE approach is evaluated through extensive simulation studies. The empirical results from simulation studies demonstrate the superiority of proposed spatial nonstationary SAE method over the nonspatial and stationary alternatives. The method is also applied to estimate paddy (green) crop yield at district level in the state of Uttar Pradesh in India using survey data from the improvement of crop statistics scheme and linked with Census data. A spatial map presents a quick view to the regional variations or disparity in district level yield estimates and are certainly helpful to the decision makers for identifying the regions and areas requiring more attention for designing targeted interventions and policy development.



中文翻译:

空间非平稳 Fay-Herriot 模型下小面积均值的分层贝叶斯估计

摘要

Fay-Herriot (FH) 模型广泛用于聚合水平数据的小区域估计 (SAE),但在一些应用中,不能否认连续或相邻区域之间存在空间效应,而该模型无法处理这一点。条件自回归和联立自回归规范确实纳入了空间关联性,同时考虑了区域之间的空间相关效应。然而,这些方法都没有通过空间相关的固定效应参数来实现空间变化协变量的想法。统计学中的这种方法称为空间非平稳性。本文介绍了考虑分层贝叶斯范式的 FH 模型的空间非平稳版本,然后考虑了小区域均值的估计。所提出的 SAE 方法通过广泛的模拟研究进行评估。模拟研究的实证结果证明了所提出的空间非平稳 SAE 方法相对于非空间和平稳替代方法的优越性。该方法还适用于利用改进作物统计方案的调查数据并与人口普查数据相联系来估算印度北方邦地区一级的水稻(绿色)作物产量。空间地图可以快速了解地区一级产量估计的区域差异或差异,并且肯定有助于决策者确定需要更多关注的地区和领域,以设计有针对性的干预措施和政策制定。模拟研究的实证结果证明了所提出的空间非平稳 SAE 方法相对于非空间和平稳替代方法的优越性。该方法还适用于利用改进作物统计方案的调查数据并与人口普查数据相联系来估算印度北方邦地区一级的水稻(绿色)作物产量。空间地图可以快速了解地区一级产量估计的区域差异或差异,并且肯定有助于决策者确定需要更多关注的地区和领域,以设计有针对性的干预措施和政策制定。模拟研究的实证结果证明了所提出的空间非平稳 SAE 方法相对于非空间和平稳替代方法的优越性。该方法还适用于利用改进作物统计方案的调查数据并与人口普查数据相联系来估算印度北方邦地区一级的水稻(绿色)作物产量。空间地图可以快速了解地区一级产量估计的区域差异或差异,并且肯定有助于决策者确定需要更多关注的地区和领域,以设计有针对性的干预措施和政策制定。该方法还适用于利用改进作物统计方案的调查数据并与人口普查数据相联系来估算印度北方邦地区一级的水稻(绿色)作物产量。空间地图可以快速了解地区一级产量估计的区域差异或差异,并且肯定有助于决策者确定需要更多关注的地区和领域,以设计有针对性的干预措施和政策制定。该方法还适用于利用改进作物统计方案的调查数据并与人口普查数据相联系来估算印度北方邦地区一级的水稻(绿色)作物产量。空间地图可以快速了解地区一级产量估计的区域差异或差异,并且肯定有助于决策者确定需要更多关注的地区和领域,以设计有针对性的干预措施和政策制定。

更新日期:2021-05-24
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