Scale invariant and efficient estimation for groupwise scaled envelope model

IF 0.6 4区 数学 Q4 STATISTICS & PROBABILITY Journal of the Korean Statistical Society Pub Date : 2024-07-14 DOI:10.1007/s42952-024-00277-0
Jing Zhang, Zhensheng Huang
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Abstract

Motivated by different groups containing different group information under the heteroscedastic error structure, we propose the groupwise scaled envelope model that is invariable to scale changes and is permissible for distinct regression coefficients and the heteroscedastic error structure across groups. It retains the potential of the scaled envelope methods to keep the scale invariant and allows for both different regression coefficients and different error structures for diverse groups. Further, we demonstrate the maximum likelihood estimators and its theoretical properties including parameter identifiability, asymptotic distribution and consistency of the groupwise scaled envelope estimator. Lastly, simulation studies and a real-data example demonstrate the advantages of the groupwise scaled envelope estimators, including a comparison with the standard model estimators, groupwise envelope estimators, scaled envelope estimators and separate scaled envelope estimators.

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分组比例包络模型的规模不变性和高效估算
在异方差误差结构下,不同群体包含不同的群体信息,受此启发,我们提出了群体比例包络模型,该模型不受规模变化的影响,允许不同群体有不同的回归系数和异方差误差结构。它保留了缩放包络法保持尺度不变的潜力,并允许不同群体有不同的回归系数和不同的误差结构。此外,我们还展示了最大似然估计器及其理论特性,包括参数可识别性、渐近分布和分组缩放包络估计器的一致性。最后,模拟研究和一个真实数据示例展示了分组缩放包络估计器的优势,包括与标准模型估计器、分组包络估计器、缩放包络估计器和单独缩放包络估计器的比较。
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来源期刊
Journal of the Korean Statistical Society
Journal of the Korean Statistical Society 数学-统计学与概率论
CiteScore
1.30
自引率
0.00%
发文量
37
审稿时长
3 months
期刊介绍: The Journal of the Korean Statistical Society publishes research articles that make original contributions to the theory and methodology of statistics and probability. It also welcomes papers on innovative applications of statistical methodology, as well as papers that give an overview of current topic of statistical research with judgements about promising directions for future work. The journal welcomes contributions from all countries.
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