{"title":"正态分布的替代Cholesky分解与尺度族混合:一种联合建模方法","authors":"Vinícius Silva Osterne Ribeiro , Lionel Bombrun , Juvêncio Santos Nobre , Charles Casimiro Cavalcante , Yannick Berthoumieu","doi":"10.1016/j.sigpro.2025.110207","DOIUrl":null,"url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":49523,"journal":{"name":"Signal Processing","volume":"238 ","pages":"Article 110207"},"PeriodicalIF":3.6000,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Alternative Cholesky Decomposition and family of scale mixture of Normal distribution: A joint modeling approach\",\"authors\":\"Vinícius Silva Osterne Ribeiro , Lionel Bombrun , Juvêncio Santos Nobre , Charles Casimiro Cavalcante , Yannick Berthoumieu\",\"doi\":\"10.1016/j.sigpro.2025.110207\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>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.</div></div>\",\"PeriodicalId\":49523,\"journal\":{\"name\":\"Signal Processing\",\"volume\":\"238 \",\"pages\":\"Article 110207\"},\"PeriodicalIF\":3.6000,\"publicationDate\":\"2025-07-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Signal Processing\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0165168425003214\",\"RegionNum\":2,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ENGINEERING, ELECTRICAL & ELECTRONIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Signal Processing","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0165168425003214","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
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.
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.