正态分布的替代Cholesky分解与尺度族混合:一种联合建模方法

IF 3.6 2区 工程技术 Q2 ENGINEERING, ELECTRICAL & ELECTRONIC
Vinícius Silva Osterne Ribeiro , Lionel Bombrun , Juvêncio Santos Nobre , Charles Casimiro Cavalcante , Yannick Berthoumieu
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引用次数: 0

摘要

在统计学中,包括生物医学和农业研究在内的各个领域的纵向数据分析是必不可少的。联合均值-协方差模型已被广泛用于捕获主体内相关性,通常通过修正Cholesky分解(MCD)对散点矩阵进行参数化。然而,MCD有一些已知的缺点,比如对变量顺序的敏感性和参数解释方面的挑战。作为一种替代方法,替代乔尔斯基分解(ACD)提供了更好的数值稳定性和可解释性,但在鲁棒建模环境中尚未得到充分探索。传统的方法也经常假设残差为正态分布,这在实践中可能不成立。虽然基于Student-t和拉普拉斯分布的扩展解决了较重的尾部,但它们仍然依赖于固定的参数形式。为了克服结构和分布的局限性,本文提出了一种结合ACD的灵活性和尺度混合正态分布(SMN)的鲁棒性的联合回归模型。我们获得了最大似然估计量,并将我们的模型与经典的和基于学生的替代方案进行了比较。仿真研究表明,在离群值污染下,该方法具有较好的估计和预测性能。实际数据应用进一步凸显了该模型的鲁棒性和实用性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Alternative Cholesky Decomposition and family of scale mixture of Normal distribution: A joint modeling approach
In Statistics, the analysis of longitudinal data is essential across various domains, including biomedical and agricultural research. Joint mean-covariance models have been widely used to capture within-subject dependence, often by parametrizing the scatter matrix via the Modified Cholesky Decomposition (MCD). However, the MCD has known drawbacks, such as sensitivity to the ordering of variables and challenges in parameter interpretation. As an alternative, the Alternative Cholesky Decomposition (ACD) offers improved numerical stability and interpretability, yet has been underexplored in robust modeling contexts. Traditional approaches also frequently assume normally distributed residuals, which may not hold in practice. While extensions based on the Student-t and Laplace distributions address heavier tails, they still rely on fixed parametric forms. To overcome both structural and distributional limitations, this paper proposes a novel joint regression model that combines the flexibility of ACD with the robustness of scale mixture of normal (SMN) distributions. We obtain maximum likelihood estimators and compare our model against classical and Student-t-based alternatives. Simulation studies show superior performance in estimation and prediction under outlier contamination. Real data applications further highlight the model’s robustness and practical utility.
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来源期刊
Signal Processing
Signal Processing 工程技术-工程:电子与电气
CiteScore
9.20
自引率
9.10%
发文量
309
审稿时长
41 days
期刊介绍: Signal Processing incorporates all aspects of the theory and practice of signal processing. It features original research work, tutorial and review articles, and accounts of practical developments. It is intended for a rapid dissemination of knowledge and experience to engineers and scientists working in the research, development or practical application of signal processing. Subject areas covered by the journal include: Signal Theory; Stochastic Processes; Detection and Estimation; Spectral Analysis; Filtering; Signal Processing Systems; Software Developments; Image Processing; Pattern Recognition; Optical Signal Processing; Digital Signal Processing; Multi-dimensional Signal Processing; Communication Signal Processing; Biomedical Signal Processing; Geophysical and Astrophysical Signal Processing; Earth Resources Signal Processing; Acoustic and Vibration Signal Processing; Data Processing; Remote Sensing; Signal Processing Technology; Radar Signal Processing; Sonar Signal Processing; Industrial Applications; New Applications.
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