This paper investigates a constrained spatial autoregressive panel data model with fixed effects, partially linear time-varying coefficients, and time-varying spatial dependence. We propose a constrained profile two-stage least squares estimator and establish its asymptotic properties. Furthermore, a statistical test is constructed to examine whether the constant coefficients satisfy pre-specified linear constraints. Monte Carlo simulations under both independent and -mixing error structures demonstrate the finite-sample performance of the proposed estimators and testing procedure. A real data example is provided to illustrate the practical applicability of the method. In addition, when the time dimension is relatively small, a Block Bootstrap procedure is proposed to compute the -value for the test.
{"title":"Estimation for partially time-varying spatial autoregressive panel data model under linear constraints","authors":"Lingling Tian , Chuanhua Wei , Bing Sun , Mixia Wu","doi":"10.1016/j.jmva.2025.105547","DOIUrl":"10.1016/j.jmva.2025.105547","url":null,"abstract":"<div><div>This paper investigates a constrained spatial autoregressive panel data model with fixed effects, partially linear time-varying coefficients, and time-varying spatial dependence. We propose a constrained profile two-stage least squares estimator and establish its asymptotic properties. Furthermore, a statistical test is constructed to examine whether the constant coefficients satisfy pre-specified linear constraints. Monte Carlo simulations under both independent and <span><math><mi>α</mi></math></span>-mixing error structures demonstrate the finite-sample performance of the proposed estimators and testing procedure. A real data example is provided to illustrate the practical applicability of the method. In addition, when the time dimension <span><math><mi>T</mi></math></span> is relatively small, a Block Bootstrap procedure is proposed to compute the <span><math><mi>p</mi></math></span>-value for the test.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"212 ","pages":"Article 105547"},"PeriodicalIF":1.4,"publicationDate":"2025-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145571182","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Covariance matrix estimation is an important problem in multivariate data analysis, both from theoretical as well as applied points of view. Many simple and popular covariance matrix estimators are known to be severely affected by model misspecification and the presence of outliers in the data; on the other hand robust estimators with reasonably high efficiency are often computationally challenging for modern large and complex datasets. In this work, we propose a new, simple, robust and highly efficient method for estimation of the location vector and the scatter matrix for elliptically symmetric distributions. The proposed estimation procedure is designed in the spirit of the minimum density power divergence (DPD) estimation approach with appropriate modifications which makes our proposal (componentwise minimum DPD estimation) computationally very economical and scalable to large as well as higher dimensional datasets. Consistency and asymptotic normality of the proposed componentwise estimators of the multivariate location and scatter are established along with asymptotic positive definiteness of the estimated scatter matrix. Robustness of our estimators are studied by means of influence functions. All theoretical results are illustrated further under multivariate normality. A large-scale simulation study is presented to assess finite sample performances and scalability of our method in comparison to the usual maximum likelihood estimator (MLE), the ordinary minimum DPD estimator (MDPDE) and other popular non-parametric methods. The applicability of our method is further illustrated with a real dataset on credit card transactions.
{"title":"A componentwise estimation procedure for multivariate location and scatter: Robustness, efficiency and scalability","authors":"Soumya Chakraborty , Ayanendranath Basu , Abhik Ghosh","doi":"10.1016/j.jmva.2025.105546","DOIUrl":"10.1016/j.jmva.2025.105546","url":null,"abstract":"<div><div>Covariance matrix estimation is an important problem in multivariate data analysis, both from theoretical as well as applied points of view. Many simple and popular covariance matrix estimators are known to be severely affected by model misspecification and the presence of outliers in the data; on the other hand robust estimators with reasonably high efficiency are often computationally challenging for modern large and complex datasets. In this work, we propose a new, simple, robust and highly efficient method for estimation of the location vector and the scatter matrix for elliptically symmetric distributions. The proposed estimation procedure is designed in the spirit of the minimum density power divergence (DPD) estimation approach with appropriate modifications which makes our proposal (componentwise minimum DPD estimation) computationally very economical and scalable to large as well as higher dimensional datasets. Consistency and asymptotic normality of the proposed componentwise estimators of the multivariate location and scatter are established along with asymptotic positive definiteness of the estimated scatter matrix. Robustness of our estimators are studied by means of influence functions. All theoretical results are illustrated further under multivariate normality. A large-scale simulation study is presented to assess finite sample performances and scalability of our method in comparison to the usual maximum likelihood estimator (MLE), the ordinary minimum DPD estimator (MDPDE) and other popular non-parametric methods. The applicability of our method is further illustrated with a real dataset on credit card transactions.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"212 ","pages":"Article 105546"},"PeriodicalIF":1.4,"publicationDate":"2025-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145616468","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-17DOI: 10.1016/j.jmva.2025.105545
Alessandro Mutti, Patrizia Semeraro
The key result of this paper is to characterize all multivariate symmetric Bernoulli distributions whose sum is minimal under the convex order. In doing so, we automatically characterize extremal negative dependence among Bernoulli variables, since multivariate distributions with minimal convex sums are known to be strongly negative dependent. Moreover, beyond its interest per se, this result provides insight into negative dependence within the class of copulas. In particular, two classes of copulas can be built from multivariate symmetric Bernoulli distributions: extremal mixture copulas and FGM copulas. We analyze the extremal negative dependence structures of copulas constructed from symmetric Bernoulli vectors with minimal convex sums and explicitly find a class of minimal dependence copulas. This analysis is completed by investigating minimal pairwise dependence measures and correlations. Our main results derive from the geometric and algebraic representations of multivariate symmetric Bernoulli distributions, which effectively encode key statistical properties.
{"title":"Symmetric Bernoulli distributions and minimal dependence copulas","authors":"Alessandro Mutti, Patrizia Semeraro","doi":"10.1016/j.jmva.2025.105545","DOIUrl":"10.1016/j.jmva.2025.105545","url":null,"abstract":"<div><div>The key result of this paper is to characterize all multivariate symmetric Bernoulli distributions whose sum is minimal under the convex order. In doing so, we automatically characterize extremal negative dependence among Bernoulli variables, since multivariate distributions with minimal convex sums are known to be strongly negative dependent. Moreover, beyond its interest per se, this result provides insight into negative dependence within the class of copulas. In particular, two classes of copulas can be built from multivariate symmetric Bernoulli distributions: extremal mixture copulas and FGM copulas. We analyze the extremal negative dependence structures of copulas constructed from symmetric Bernoulli vectors with minimal convex sums and explicitly find a class of minimal dependence copulas. This analysis is completed by investigating minimal pairwise dependence measures and correlations. Our main results derive from the geometric and algebraic representations of multivariate symmetric Bernoulli distributions, which effectively encode key statistical properties.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"212 ","pages":"Article 105545"},"PeriodicalIF":1.4,"publicationDate":"2025-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145537556","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-17DOI: 10.1016/j.jmva.2025.105544
Jiajie Lu, Xiaohu Li
In this study, we investigate both sufficient and necessary conditions for bivariate skew-normal distributions to be stochastic arrangement increasing. The main results serve as either natural extension of or nice supplement to the characterization result of this property for bivariate normal distributions due to Cai and Wei (2015). Also, we generalize these results to multivariate skew-normal distributions. Numerical examples based on the theory and a real data are presented to illustrate the main results as well.
{"title":"Stochastic arrangement increasing property of skew-normal distributions","authors":"Jiajie Lu, Xiaohu Li","doi":"10.1016/j.jmva.2025.105544","DOIUrl":"10.1016/j.jmva.2025.105544","url":null,"abstract":"<div><div>In this study, we investigate both sufficient and necessary conditions for bivariate skew-normal distributions to be stochastic arrangement increasing. The main results serve as either natural extension of or nice supplement to the characterization result of this property for bivariate normal distributions due to Cai and Wei (2015). Also, we generalize these results to multivariate skew-normal distributions. Numerical examples based on the theory and a real data are presented to illustrate the main results as well.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"212 ","pages":"Article 105544"},"PeriodicalIF":1.4,"publicationDate":"2025-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145537557","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-15DOI: 10.1016/j.jmva.2025.105530
Martin Eppert , Satyaki Mukherjee , Debarghya Ghoshdastidar
Projection Pursuit is a classic exploratory technique for finding interesting projections of a dataset. We propose a method for recovering projections containing either Imbalanced Clusters or a Bernoulli–Rademacher distribution using a gradient-based technique to optimize the projection index. As sample complexity is a major limiting factor in Projection Pursuit, we analyze our algorithm’s sample complexity within a Planted Vector setting where we can observe that Imbalanced Clusters can be recovered more easily than balanced ones. Additionally, we give a generalized result that works for a variety of data distributions and projection indices. We compare these results to computational lower bounds in the Low-Degree-Polynomial Framework. Finally, we experimentally evaluate our method’s applicability to real-world data using FashionMNIST and the Human Activity Recognition Dataset, where our algorithm outperforms others when only a few samples are available.
{"title":"Recovering Imbalanced Clusters via gradient-based projection pursuit","authors":"Martin Eppert , Satyaki Mukherjee , Debarghya Ghoshdastidar","doi":"10.1016/j.jmva.2025.105530","DOIUrl":"10.1016/j.jmva.2025.105530","url":null,"abstract":"<div><div>Projection Pursuit is a classic exploratory technique for finding interesting projections of a dataset. We propose a method for recovering projections containing either Imbalanced Clusters or a Bernoulli–Rademacher distribution using a gradient-based technique to optimize the projection index. As sample complexity is a major limiting factor in Projection Pursuit, we analyze our algorithm’s sample complexity within a Planted Vector setting where we can observe that Imbalanced Clusters can be recovered more easily than balanced ones. Additionally, we give a generalized result that works for a variety of data distributions and projection indices. We compare these results to computational lower bounds in the Low-Degree-Polynomial Framework. Finally, we experimentally evaluate our method’s applicability to real-world data using FashionMNIST and the Human Activity Recognition Dataset, where our algorithm outperforms others when only a few samples are available.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"212 ","pages":"Article 105530"},"PeriodicalIF":1.4,"publicationDate":"2025-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145616469","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The high dimensionality of the input data can pose multiple problems when implementing statistical techniques. The presence of many dimensions in the data can lead to challenges in visualizing the data, higher computational demands, and a higher probability of over-fitting or under-fitting in modeling. Furthermore, the curse of dimensionality contributes to these issues by stating that the necessary number of observations for accurate modeling increases exponentially as the number of dimensions increases. Dimension reduction tools help overcome this challenge. Principal Component Analysis (PCA) is the most widely used technique, intensively studied in classical linear spaces. However, in applied sciences such as biology, bioinformatics, astronomy and geology, there are many instances in which the data’s support are non-Euclidean spaces. In fact, the available data often include elements of Riemannian manifolds such as the unit circle, torus, sphere, and their extensions. Therefore, the terms “manifold-valued” or “directional” data are used in the literature for these situations. When dealing with directional data, the linear nature of PCA might pose a challenge to achieve accurate data reduction. This paper therefore reviews and investigates the methodological aspects of PCA on directional data and their practical applications.
{"title":"Recent advances in principal component analysis for directional data","authors":"Anahita Nodehi , Meisam Moghimbeygi , Christophe Ley","doi":"10.1016/j.jmva.2025.105528","DOIUrl":"10.1016/j.jmva.2025.105528","url":null,"abstract":"<div><div>The high dimensionality of the input data can pose multiple problems when implementing statistical techniques. The presence of many dimensions in the data can lead to challenges in visualizing the data, higher computational demands, and a higher probability of over-fitting or under-fitting in modeling. Furthermore, the curse of dimensionality contributes to these issues by stating that the necessary number of observations for accurate modeling increases exponentially as the number of dimensions increases. Dimension reduction tools help overcome this challenge. Principal Component Analysis (PCA) is the most widely used technique, intensively studied in classical linear spaces. However, in applied sciences such as biology, bioinformatics, astronomy and geology, there are many instances in which the data’s support are non-Euclidean spaces. In fact, the available data often include elements of Riemannian manifolds such as the unit circle, torus, sphere, and their extensions. Therefore, the terms “manifold-valued” or “directional” data are used in the literature for these situations. When dealing with directional data, the linear nature of PCA might pose a challenge to achieve accurate data reduction. This paper therefore reviews and investigates the methodological aspects of PCA on directional data and their practical applications.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"212 ","pages":"Article 105528"},"PeriodicalIF":1.4,"publicationDate":"2025-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145537554","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-15DOI: 10.1016/j.jmva.2025.105526
Rou Zhong , Jingxiao Zhang , Chunming Zhang
Functional principal component analysis (FPCA) is an important technique for dimension reduction in functional data analysis (FDA). Classical FPCA method is based on the Karhunen-Loève expansion, which assumes a linear structure of the observed functional data. However, the assumption may not always be satisfied, and the FPCA method can become inefficient when the data deviates from the linear assumption. In this paper, we propose a novel FPCA method that is suitable for data with a nonlinear structure with the use of neural networks. We construct networks that can be applied to functional data and explore the corresponding universal approximation property. The main use of our proposed nonlinear FPCA method is curve reconstruction. We conduct a simulation study to evaluate the performance of our method. The proposed method is also applied to a real-world data set to further demonstrate its superiority.
{"title":"Nonlinear functional principal component analysis using neural networks","authors":"Rou Zhong , Jingxiao Zhang , Chunming Zhang","doi":"10.1016/j.jmva.2025.105526","DOIUrl":"10.1016/j.jmva.2025.105526","url":null,"abstract":"<div><div>Functional principal component analysis (FPCA) is an important technique for dimension reduction in functional data analysis (FDA). Classical FPCA method is based on the Karhunen-Loève expansion, which assumes a linear structure of the observed functional data. However, the assumption may not always be satisfied, and the FPCA method can become inefficient when the data deviates from the linear assumption. In this paper, we propose a novel FPCA method that is suitable for data with a nonlinear structure with the use of neural networks. We construct networks that can be applied to functional data and explore the corresponding universal approximation property. The main use of our proposed nonlinear FPCA method is curve reconstruction. We conduct a simulation study to evaluate the performance of our method. The proposed method is also applied to a real-world data set to further demonstrate its superiority.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"212 ","pages":"Article 105526"},"PeriodicalIF":1.4,"publicationDate":"2025-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145537559","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-14DOI: 10.1016/j.jmva.2025.105540
Abhijit Mandal , Samiran Ghosh
We develop a robust variable selection framework that integrates divergence-based M-estimation with penalization. The proposed method yields regression parameter estimates that are resistant to outliers while simultaneously identifying the most relevant explanatory variables. The asymptotic distribution and influence function of the estimators are derived. Classical model selection criteria such as Mallows’ and the Akaike information criterion (AIC) are known to deteriorate under heavy-tailed errors or contamination. To address this issue, we introduce robust counterparts of these criteria, constructed from our divergence-based estimators. The proposed approach substantially improves variable selection and prediction performance in the presence of outliers, while maintaining competitiveness with state-of-the-art robust high-dimensional methods. The practical utility of the procedure is further demonstrated through an analysis of the plasma Beta-Carotene dataset.
{"title":"Robust variable selection criteria for the penalized regression","authors":"Abhijit Mandal , Samiran Ghosh","doi":"10.1016/j.jmva.2025.105540","DOIUrl":"10.1016/j.jmva.2025.105540","url":null,"abstract":"<div><div>We develop a robust variable selection framework that integrates divergence-based M-estimation with penalization. The proposed method yields regression parameter estimates that are resistant to outliers while simultaneously identifying the most relevant explanatory variables. The asymptotic distribution and influence function of the estimators are derived. Classical model selection criteria such as Mallows’ <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> and the Akaike information criterion (AIC) are known to deteriorate under heavy-tailed errors or contamination. To address this issue, we introduce robust counterparts of these criteria, constructed from our divergence-based estimators. The proposed approach substantially improves variable selection and prediction performance in the presence of outliers, while maintaining competitiveness with state-of-the-art robust high-dimensional methods. The practical utility of the procedure is further demonstrated through an analysis of the plasma Beta-Carotene dataset.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"211 ","pages":"Article 105540"},"PeriodicalIF":1.4,"publicationDate":"2025-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145516865","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-14DOI: 10.1016/j.jmva.2025.105543
Runfei Luo , Anna Liu , Hao Dong , Yuedong Wang
Density estimation and graphical models play important roles in statistical learning. The estimated density can be used to construct a graphical model that reveals conditional relationships, whereas a graphical structure can be used to build models for density estimation. We propose a semiparametric framework that models part of the density function nonparametrically using a smoothing spline ANOVA (SS ANOVA) model and the conditional density parametrically using a conditional Gaussian graphical model (cGGM). This flexible framework allows us to deal with high-dimensional data without the Gaussian assumption. We develop computationally efficient algorithms for estimation and provide theoretical guarantees for our procedure. Our experimental results show that the proposed framework outperforms both parametric and nonparametric baselines.
{"title":"Density and graph estimation with smoothing splines and conditional Gaussian graphical models","authors":"Runfei Luo , Anna Liu , Hao Dong , Yuedong Wang","doi":"10.1016/j.jmva.2025.105543","DOIUrl":"10.1016/j.jmva.2025.105543","url":null,"abstract":"<div><div>Density estimation and graphical models play important roles in statistical learning. The estimated density can be used to construct a graphical model that reveals conditional relationships, whereas a graphical structure can be used to build models for density estimation. We propose a semiparametric framework that models part of the density function nonparametrically using a smoothing spline ANOVA (SS ANOVA) model and the conditional density parametrically using a conditional Gaussian graphical model (cGGM). This flexible framework allows us to deal with high-dimensional data without the Gaussian assumption. We develop computationally efficient algorithms for estimation and provide theoretical guarantees for our procedure. Our experimental results show that the proposed framework outperforms both parametric and nonparametric baselines.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"212 ","pages":"Article 105543"},"PeriodicalIF":1.4,"publicationDate":"2025-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145537555","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-13DOI: 10.1016/j.jmva.2025.105525
Steven Golovkine , Edward Gunning , Andrew J. Simpkin , Norma Bargary
Dimension reduction is crucial in functional data analysis (FDA). The key tool to reduce the dimension of the data is functional principal component analysis. Existing approaches for functional principal component analysis usually involve the diagonalization of the covariance operator. With the increasing size and complexity of functional datasets, estimating the covariance operator has become more challenging. Therefore, there is a growing need for efficient methodologies to estimate the eigencomponents. Using the duality of the space of observations and the space of functional features, we propose to use the inner-product between the curves to estimate the eigenelements of multivariate and multidimensional functional datasets. The relationship between the eigenelements of the covariance operator and those of the inner-product matrix is established. We explore the application of these methodologies in several FDA settings and provide general guidance on their usability.
{"title":"On the use of the Gram matrix for multivariate functional principal components analysis","authors":"Steven Golovkine , Edward Gunning , Andrew J. Simpkin , Norma Bargary","doi":"10.1016/j.jmva.2025.105525","DOIUrl":"10.1016/j.jmva.2025.105525","url":null,"abstract":"<div><div>Dimension reduction is crucial in functional data analysis (FDA). The key tool to reduce the dimension of the data is functional principal component analysis. Existing approaches for functional principal component analysis usually involve the diagonalization of the covariance operator. With the increasing size and complexity of functional datasets, estimating the covariance operator has become more challenging. Therefore, there is a growing need for efficient methodologies to estimate the eigencomponents. Using the duality of the space of observations and the space of functional features, we propose to use the inner-product between the curves to estimate the eigenelements of multivariate and multidimensional functional datasets. The relationship between the eigenelements of the covariance operator and those of the inner-product matrix is established. We explore the application of these methodologies in several FDA settings and provide general guidance on their usability.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"212 ","pages":"Article 105525"},"PeriodicalIF":1.4,"publicationDate":"2025-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145681886","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号