Robust Bayesian small area estimation using the sub-Gaussian $$\alpha$$ -stable distribution for measurement error in covariates

IF 1.4 4区数学 Q2 STATISTICS & PROBABILITY

Asta-Advances in Statistical Analysis Pub Date : 2024-03-06 DOI:10.1007/s10182-024-00493-3

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引用次数: 0

Abstract

In small area estimation, the sample size is so small that direct estimators have seldom enough adequate precision. Therefore, it is common to use auxiliary data via covariates and produce estimators that combine them with direct data. Nevertheless, it is not uncommon for covariates to be measured with error, leading to inconsistent estimators. Area-level models accounting for measurement error (ME) in covariates have been proposed, and they usually assume that the errors are an i.i.d. Gaussian model. However, there might be situations in which this assumption is violated especially when covariates present severe outlying values that cannot be cached by the Gaussian distribution. To overcome this problem, we propose to model the ME through sub-Gaussian $\alpha$ -stable (SG $\alpha$ S) distribution, a flexible distribution that accommodates different types of outlying observations and also Gaussian data as a special case when $\alpha =2$ . The SG $\alpha$ S distribution is a generalization of the Gaussian distribution that allows for skewness and heavy tails by adding an extra parameter, $\alpha \in (0,2]$ , to control tail behaviour. The model parameters are estimated in a fully Bayesian framework. The performance of the proposal is illustrated by applying to real data and some simulation studies.

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使用亚高斯$$\alpha$$-稳定分布对协变因素中的测量误差进行稳健的贝叶斯小面积估算

摘要在小面积估算中，样本量非常小，直接估算器很少有足够的精度。因此，通常通过协变量使用辅助数据，并将其与直接数据结合生成估算器。然而，协变量的测量存在误差，导致估计值不一致的情况并不少见。有人提出了考虑协变量测量误差（ME）的区域级模型，这些模型通常假设误差为 i.i.d. 高斯模型。然而，在某些情况下，这一假设可能会被违反，尤其是当协变量出现严重的离群值，而高斯分布无法将其缓存时。为了克服这个问题，我们建议通过亚高斯稳定分布（SG $\alpha$ S）对 ME 进行建模，这是一种灵活的分布，可以容纳不同类型的离差观测值，当 $\alpha =2$时，高斯数据也是一种特殊情况。SG $\alpha$ S 分布是高斯分布的广义化，通过增加一个额外参数（(0,2]\）来控制尾部行为，从而允许偏斜和重尾。模型参数在完全贝叶斯框架下进行估计。通过应用真实数据和一些模拟研究，说明了该建议的性能。

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来源期刊

Asta-Advances in Statistical Analysis 数学-统计学与概率论

CiteScore

2.20

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： AStA - Advances in Statistical Analysis, a journal of the German Statistical Society, is published quarterly and presents original contributions on statistical methods and applications and review articles.