Pub Date : 2025-10-10DOI: 10.1016/j.jmva.2025.105514
Min Xu , Qi-Hang Zhou , Qin Fang , Zhuo-Xi Shi
We investigate the Nyström method as an efficient means of overcoming the computational bottleneck inherent in estimating the singular functions of kernel cross-covariance operators, which play a central role in tasks such as covariate shift correction and multi-view learning. We present a Nyström-type approximation of the kernel cross-covariance operator, and establish its convergence rate. Furthermore, we derive a novel bound on the weighted sum of squared estimation errors of all associated singular functions, providing tighter control than traditional bounds that treat each error individually. Our theoretical analysis reveals that the Nyström-based singular function estimators attain the same statistical accuracy as their full empirical counterparts, while offering significant computational savings. Numerical experiments further confirm the practical effectiveness of the proposed approach.
{"title":"Estimating singular functions of kernel cross-covariance operators: An investigation of the Nyström method","authors":"Min Xu , Qi-Hang Zhou , Qin Fang , Zhuo-Xi Shi","doi":"10.1016/j.jmva.2025.105514","DOIUrl":"10.1016/j.jmva.2025.105514","url":null,"abstract":"<div><div>We investigate the Nyström method as an efficient means of overcoming the computational bottleneck inherent in estimating the singular functions of kernel cross-covariance operators, which play a central role in tasks such as covariate shift correction and multi-view learning. We present a Nyström-type approximation of the kernel cross-covariance operator, and establish its convergence rate. Furthermore, we derive a novel bound on the weighted sum of squared estimation errors of all associated singular functions, providing tighter control than traditional bounds that treat each error individually. Our theoretical analysis reveals that the Nyström-based singular function estimators attain the same statistical accuracy as their full empirical counterparts, while offering significant computational savings. Numerical experiments further confirm the practical effectiveness of the proposed approach.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"211 ","pages":"Article 105514"},"PeriodicalIF":1.4,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145266689","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}
We introduce model-based Fréchet regression in metric spaces. Instead of starting from point-wise conditional Fréchet means, our approach is defined as a constrained minimization problem over a model class of functions. The approach is then applied to develop a general framework of regression for quotient metric spaces with distances induced by isometric group actions. Such spaces arise naturally in applications where objects are considered equivalent up to transformations. We first establish general existence and consistency results for model-based Fréchet regression, with our quotient space regression model as a special case. As an important example we consider regression for elastic curves in the square-root velocity framework. This addresses data such as handwritten letters, movement paths, or outlines of objects, where only the image but not the parametrization of the curves is of interest. To handle sparsely or irregularly sampled curves, we model smooth conditional mean curves using splines. We validate our approach through simulations and an application to hippocampal outlines extracted from Magnetic Resonance Imaging scans. Here we model how the shape of the irregularly sampled hippocampus is related to age, Alzheimer’s disease and sex, to disentangle the shrinking effects of Alzheimer’s from normal aging.
{"title":"Model-based Fréchet regression in (quotient) metric spaces with a focus on elastic curves","authors":"Lisa Steyer , Almond Stöcker , Sonja Greven , Alzheimer’s Disease Neuroimaging Initiative","doi":"10.1016/j.jmva.2025.105515","DOIUrl":"10.1016/j.jmva.2025.105515","url":null,"abstract":"<div><div>We introduce model-based Fréchet regression in metric spaces. Instead of starting from point-wise conditional Fréchet means, our approach is defined as a constrained minimization problem over a model class of functions. The approach is then applied to develop a general framework of regression for quotient metric spaces with distances induced by isometric group actions. Such spaces arise naturally in applications where objects are considered equivalent up to transformations. We first establish general existence and consistency results for model-based Fréchet regression, with our quotient space regression model as a special case. As an important example we consider regression for elastic curves in the square-root velocity framework. This addresses data such as handwritten letters, movement paths, or outlines of objects, where only the image but not the parametrization of the curves is of interest. To handle sparsely or irregularly sampled curves, we model smooth conditional mean curves using splines. We validate our approach through simulations and an application to hippocampal outlines extracted from Magnetic Resonance Imaging scans. Here we model how the shape of the irregularly sampled hippocampus is related to age, Alzheimer’s disease and sex, to disentangle the shrinking effects of Alzheimer’s from normal aging.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"211 ","pages":"Article 105515"},"PeriodicalIF":1.4,"publicationDate":"2025-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145321069","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 : 2025-10-06DOI: 10.1016/j.jmva.2025.105513
Youming Liu , Li Miao
Estimation of covariance matrices plays an important role in high-dimensional inference problems. It has been investigated when some observations are missing. The known work usually assume the Gaussian or sub-Gaussian condition of a random vector. Cai and Zhang provide an optimal estimation for a class of sparse covariance matrices under the sub-Gaussian assumption of a random vector, see T. T. Cai and A. Zhang, Journal of Multivariate Analysis, 2016. This current paper considers the same problem for a larger family of sparse covariance matrices under some weaker assumptions (not necessarily sub-Gaussian) of a random vector. When , our results generalize a theorem of Cai and Zhang. Numerical experiments are given to support our theoretical analysis.
{"title":"Optimal estimation for a family of sparse covariance matrices with missing data","authors":"Youming Liu , Li Miao","doi":"10.1016/j.jmva.2025.105513","DOIUrl":"10.1016/j.jmva.2025.105513","url":null,"abstract":"<div><div>Estimation of covariance matrices plays an important role in high-dimensional inference problems. It has been investigated when some observations are missing. The known work usually assume the Gaussian or sub-Gaussian condition of a random vector. Cai and Zhang provide an optimal estimation for a class of sparse covariance matrices <span><math><mi>H</mi></math></span> under the sub-Gaussian assumption of a random vector, see T. T. Cai and A. Zhang, Journal of Multivariate Analysis, 2016. This current paper considers the same problem for a larger family of sparse covariance matrices <span><math><mrow><msub><mrow><mi>H</mi></mrow><mrow><mi>ɛ</mi></mrow></msub><mspace></mspace><mrow><mo>(</mo><mn>0</mn><mo><</mo><mi>ɛ</mi><mo>≤</mo><mn>2</mn><mo>)</mo></mrow></mrow></math></span> under some weaker assumptions (not necessarily sub-Gaussian) of a random vector. When <span><math><mrow><mi>ɛ</mi><mo>=</mo><mn>2</mn></mrow></math></span>, our results generalize a theorem of Cai and Zhang. Numerical experiments are given to support our theoretical analysis.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"211 ","pages":"Article 105513"},"PeriodicalIF":1.4,"publicationDate":"2025-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145321070","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 : 2025-09-29DOI: 10.1016/j.jmva.2025.105510
Xiaoting Li, Harry Joe
The theoretical properties of two widely used CoVaR definitions are investigated under different dependence structures in joint distributions. By using copulas, the dependence is separated from marginal distributions, and CoVaR is expressed through an adjustment factor based solely on the copula. The primary contribution is to study the limiting behavior of the adjustment factor and its link to the strength of dependence in the tails of the joint distribution. We also provide asymptotic results for bivariate Archimedean copulas and extend these findings to extreme value copulas and their mixtures. These findings enhance the understanding of CoVaR in risk scenarios, particularly as the conditional event becomes more extreme.
{"title":"Properties of CoVaR based on tail expansions of copulas","authors":"Xiaoting Li, Harry Joe","doi":"10.1016/j.jmva.2025.105510","DOIUrl":"10.1016/j.jmva.2025.105510","url":null,"abstract":"<div><div>The theoretical properties of two widely used CoVaR definitions are investigated under different dependence structures in joint distributions. By using copulas, the dependence is separated from marginal distributions, and CoVaR is expressed through an adjustment factor based solely on the copula. The primary contribution is to study the limiting behavior of the adjustment factor and its link to the strength of dependence in the tails of the joint distribution. We also provide asymptotic results for bivariate Archimedean copulas and extend these findings to extreme value copulas and their mixtures. These findings enhance the understanding of CoVaR in risk scenarios, particularly as the conditional event becomes more extreme.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"211 ","pages":"Article 105510"},"PeriodicalIF":1.4,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145266692","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 : 2025-09-25DOI: 10.1016/j.jmva.2025.105512
Xin Zhang , Wenbiao Zhao , Lixing Zhu
The statistical analysis of tensor-valued data has emerged as an area of increasing methodological focus. Tensor decomposition models and low-rank tensor regression models often assume that there exists a low-rank structure of the tensor data or tensor coefficient. Consistent selection of structural dimensions or tensor ranks constitutes a problem of significant theoretical and practical importance. This paper introduces a unified framework for addressing this challenge, applicable across multiple tensor decomposition frameworks and envelope regression models.
{"title":"Dimension selection in tensor decompositions and envelope models","authors":"Xin Zhang , Wenbiao Zhao , Lixing Zhu","doi":"10.1016/j.jmva.2025.105512","DOIUrl":"10.1016/j.jmva.2025.105512","url":null,"abstract":"<div><div>The statistical analysis of tensor-valued data has emerged as an area of increasing methodological focus. Tensor decomposition models and low-rank tensor regression models often assume that there exists a low-rank structure of the tensor data or tensor coefficient. Consistent selection of structural dimensions or tensor ranks constitutes a problem of significant theoretical and practical importance. This paper introduces a unified framework for addressing this challenge, applicable across multiple tensor decomposition frameworks and envelope regression models.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"211 ","pages":"Article 105512"},"PeriodicalIF":1.4,"publicationDate":"2025-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145321071","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}
Multi-view data clustering is pivotal for comprehending the heterogeneous structure of data by integrating information from diverse aspects. Nevertheless, practical challenges arise due to the differences in the granularity from different views, resulting in a hierarchical clustering structure within these distinct data types. In this work, we consider such structure information and propose a novel high-dimensional multi-view clustering approach with a hierarchical structure across views. The proposed non-convex problem is effectively tackled using the Alternating Direction Method of Multipliers algorithm, and we establish the statistical properties of the estimator. Simulation results demonstrate the effectiveness and superiority of our proposed method. In the analysis of the histopathological imaging data and gene expression data related to lung adenocarcinoma, our method unveils a hierarchical clustering structure that significantly diverges from alternative approaches.
{"title":"Hierarchical structure-guided high-dimensional multi-view clustering","authors":"Jiajia Jiang , Kuangnan Fang , Shuangge Ma , Qingzhao Zhang","doi":"10.1016/j.jmva.2025.105488","DOIUrl":"10.1016/j.jmva.2025.105488","url":null,"abstract":"<div><div>Multi-view data clustering is pivotal for comprehending the heterogeneous structure of data by integrating information from diverse aspects. Nevertheless, practical challenges arise due to the differences in the granularity from different views, resulting in a hierarchical clustering structure within these distinct data types. In this work, we consider such structure information and propose a novel high-dimensional multi-view clustering approach with a hierarchical structure across views. The proposed non-convex problem is effectively tackled using the Alternating Direction Method of Multipliers algorithm, and we establish the statistical properties of the estimator. Simulation results demonstrate the effectiveness and superiority of our proposed method. In the analysis of the histopathological imaging data and gene expression data related to lung adenocarcinoma, our method unveils a hierarchical clustering structure that significantly diverges from alternative approaches.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"211 ","pages":"Article 105488"},"PeriodicalIF":1.4,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145155083","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 : 2025-09-24DOI: 10.1016/j.jmva.2025.105511
Hui Chen , Yinxu Jia
In this article, we identify differential networks within the Gaussian graphical model framework by examining the equivalence of two precision matrices. It is challenging work when the dimension of the precision matrix increases with the sample size. Existing methods typically assume sparsity in the precision matrix structure, a condition often unmet in real data. To address this issue, we introduce a statistic based on debiased estimator of the high-dimensional precision matrix and employ multiplier bootstrap to approximate the null distribution of the proposed statistic. The proposed method can be easily coupled with various estimation algorithms for high-dimensional precision matrix. In comparison with existing methods, the superiority of the proposed approach lies in mild structure constraints to the unknown precision matrix, making it robust to intricate conditional dependence structures in real data. Additionally, we introduce a cross-fitting procedure that utilizes full data information, leading to enhanced statistical power. Theoretical justification is provided to ensure the validity of the proposed method without restrictive assumptions. We showcase the effectiveness of our proposed method by simulation and real data example, which provides evidence of the proposed method’s usefulness and potential for application in various domains.
{"title":"Identifying differential networks through high-dimensional two-sample inference","authors":"Hui Chen , Yinxu Jia","doi":"10.1016/j.jmva.2025.105511","DOIUrl":"10.1016/j.jmva.2025.105511","url":null,"abstract":"<div><div>In this article, we identify differential networks within the Gaussian graphical model framework by examining the equivalence of two precision matrices. It is challenging work when the dimension of the precision matrix increases with the sample size. Existing methods typically assume sparsity in the precision matrix structure, a condition often unmet in real data. To address this issue, we introduce a statistic based on debiased estimator of the high-dimensional precision matrix and employ multiplier bootstrap to approximate the null distribution of the proposed statistic. The proposed method can be easily coupled with various estimation algorithms for high-dimensional precision matrix. In comparison with existing methods, the superiority of the proposed approach lies in mild structure constraints to the unknown precision matrix, making it robust to intricate conditional dependence structures in real data. Additionally, we introduce a cross-fitting procedure that utilizes full data information, leading to enhanced statistical power. Theoretical justification is provided to ensure the validity of the proposed method without restrictive assumptions. We showcase the effectiveness of our proposed method by simulation and real data example, which provides evidence of the proposed method’s usefulness and potential for application in various domains.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"211 ","pages":"Article 105511"},"PeriodicalIF":1.4,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145266690","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 : 2025-09-23DOI: 10.1016/j.jmva.2025.105509
Jongik Chung , Qihu Zhang , Jennifer E. Mcdowell , Cheolwoo Park
We present methods for estimating multiple precision matrices for high-dimensional time series within the framework of Gaussian graphical models, with a specific focus on analyzing functional magnetic resonance imaging (fMRI) data collected from multiple subjects. Our goal is to estimate both individual brain networks and a collective structure representing a group of subjects. To achieve this, we propose a method that utilizes group Graphical Lasso and regularized aggregation to simultaneously estimate individual and group precision matrices, assigning varying weights to each individual based on their outlier status within the group. We investigate the convergence rates of precision matrix estimators under various norms and expectations, assessing their performance with sub-Gaussian and heavy-tailed data. The effectiveness of our methods is demonstrated through simulations and real fMRI data analysis.
{"title":"Joint graphical lasso with regularized aggregation","authors":"Jongik Chung , Qihu Zhang , Jennifer E. Mcdowell , Cheolwoo Park","doi":"10.1016/j.jmva.2025.105509","DOIUrl":"10.1016/j.jmva.2025.105509","url":null,"abstract":"<div><div>We present methods for estimating multiple precision matrices for high-dimensional time series within the framework of Gaussian graphical models, with a specific focus on analyzing functional magnetic resonance imaging (fMRI) data collected from multiple subjects. Our goal is to estimate both individual brain networks and a collective structure representing a group of subjects. To achieve this, we propose a method that utilizes group Graphical Lasso and regularized aggregation to simultaneously estimate individual and group precision matrices, assigning varying weights to each individual based on their outlier status within the group. We investigate the convergence rates of precision matrix estimators under various norms and expectations, assessing their performance with sub-Gaussian and heavy-tailed data. The effectiveness of our methods is demonstrated through simulations and real fMRI data analysis.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"211 ","pages":"Article 105509"},"PeriodicalIF":1.4,"publicationDate":"2025-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145266691","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 : 2025-09-19DOI: 10.1016/j.jmva.2025.105508
Zhengyu Zhu , Jicai Liu , Riquan Zhang
In this paper, we introduce a novel sample martingale difference correlation via data splitting to measure the departure of conditional mean independence between a response variable and a vector predictor . The proposed correlation converges to zero and has an asymptotically symmetric sampling distribution around zero when and are conditionally mean independent. In contrast, it converges to a positive value when and are conditionally mean dependent. Leveraging these properties, we develop a new model-free feature screening method with false discovery rate (FDR) control for ultrahigh-dimensional data. We demonstrate that this screening method achieves FDR control and the sure screening property simultaneously. We also extend our approach to conditional quantile screening with FDR control. To further enhance the stability of the screening results, we implement multiple splitting techniques. We evaluate the finite sample performance of our proposed methods through simulations and real data analyses, and compare them with existing methods.
{"title":"A novel martingale difference correlation via data splitting with applications in feature screening","authors":"Zhengyu Zhu , Jicai Liu , Riquan Zhang","doi":"10.1016/j.jmva.2025.105508","DOIUrl":"10.1016/j.jmva.2025.105508","url":null,"abstract":"<div><div>In this paper, we introduce a novel sample martingale difference correlation via data splitting to measure the departure of conditional mean independence between a response variable <span><math><mi>Y</mi></math></span> and a vector predictor <span><math><mi>X</mi></math></span>. The proposed correlation converges to zero and has an asymptotically symmetric sampling distribution around zero when <span><math><mi>Y</mi></math></span> and <span><math><mi>X</mi></math></span> are conditionally mean independent. In contrast, it converges to a positive value when <span><math><mi>Y</mi></math></span> and <span><math><mi>X</mi></math></span> are conditionally mean dependent. Leveraging these properties, we develop a new model-free feature screening method with false discovery rate (FDR) control for ultrahigh-dimensional data. We demonstrate that this screening method achieves FDR control and the sure screening property simultaneously. We also extend our approach to conditional quantile screening with FDR control. To further enhance the stability of the screening results, we implement multiple splitting techniques. We evaluate the finite sample performance of our proposed methods through simulations and real data analyses, and compare them with existing methods.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"211 ","pages":"Article 105508"},"PeriodicalIF":1.4,"publicationDate":"2025-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145096561","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 : 2025-09-17DOI: 10.1016/j.jmva.2025.105497
Majid Mojirsheibani
In this work we consider the problem of nonparametric estimation of a regression function with the functional covariate when the response may be missing according to a missing-not-at-random (MNAR) setup, i.e., when the underlying missing probability mechanism can depend on both and . Our proposed estimator is based on a particular representation of the regression function in terms of four associated conditional expectations that can be estimated nonparametrically. To assess the theoretical performance of our estimators, we study their convergence properties in general norms where we also look into their rates of convergence. Our numerical results show that the proposed estimators have good finite-sample performance. We also explore the applications of our results to the problem of statistical classification with missing labels and establish a number of convergence results for new kernel-type classification rules.
{"title":"On nonparametric functional data regression with incomplete observations","authors":"Majid Mojirsheibani","doi":"10.1016/j.jmva.2025.105497","DOIUrl":"10.1016/j.jmva.2025.105497","url":null,"abstract":"<div><div>In this work we consider the problem of nonparametric estimation of a regression function <span><math><mrow><mi>m</mi><mrow><mo>(</mo><mi>χ</mi><mo>)</mo></mrow><mo>=</mo><mi>E</mi><mrow><mo>(</mo><mi>Y</mi><mo>|</mo><mspace></mspace><mi>χ</mi><mo>=</mo><mi>χ</mi><mo>)</mo></mrow></mrow></math></span> with the functional covariate <span><math><mrow><mi>χ</mi></mrow></math></span> when the response <span><math><mi>Y</mi></math></span> may be missing according to a missing-not-at-random (MNAR) setup, i.e., when the underlying missing probability mechanism can depend on both <span><math><mrow><mi>χ</mi></mrow></math></span> and <span><math><mi>Y</mi></math></span>. Our proposed estimator is based on a particular representation of the regression function <span><math><mrow><mi>m</mi><mrow><mo>(</mo><mi>χ</mi><mo>)</mo></mrow></mrow></math></span> in terms of four associated conditional expectations that can be estimated nonparametrically. To assess the theoretical performance of our estimators, we study their convergence properties in general <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> norms where we also look into their rates of convergence. Our numerical results show that the proposed estimators have good finite-sample performance. We also explore the applications of our results to the problem of statistical classification with missing labels and establish a number of convergence results for new kernel-type classification rules.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"211 ","pages":"Article 105497"},"PeriodicalIF":1.4,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145096559","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}
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