Pub Date : 2024-12-15DOI: 10.1016/j.jmva.2024.105401
Weihao Yu , Qi Zhang , Weiyu Li
In bioinformation and medicine, an enormous amount of high-dimensional multi-population data is collected. For the inference of several-samples mean problem, traditional tests do not perform well and many new theories mainly focus on normal distribution and low correlation assumptions. Motivated by the weighted sign test, we propose two projection-based tests which are robust against the choice of correlation matrix. One test utilizes Scheffe’s transformation to generate a group of new samples and derives the optimal projection direction. The other test is adaptive to projection direction and is generalized to the assumption of the whole elliptical distribution and independent component model. Further the theoretical properties are deduced and numerical experiments are carried out to examine the finite sample performance. They show that our tests outperform others under certain circumstances.
{"title":"High-dimensional projection-based ANOVA test","authors":"Weihao Yu , Qi Zhang , Weiyu Li","doi":"10.1016/j.jmva.2024.105401","DOIUrl":"10.1016/j.jmva.2024.105401","url":null,"abstract":"<div><div>In bioinformation and medicine, an enormous amount of high-dimensional multi-population data is collected. For the inference of several-samples mean problem, traditional tests do not perform well and many new theories mainly focus on normal distribution and low correlation assumptions. Motivated by the weighted sign test, we propose two projection-based tests which are robust against the choice of correlation matrix. One test utilizes Scheffe’s transformation to generate a group of new samples and derives the optimal projection direction. The other test is adaptive to projection direction and is generalized to the assumption of the whole elliptical distribution and independent component model. Further the theoretical properties are deduced and numerical experiments are carried out to examine the finite sample performance. They show that our tests outperform others under certain circumstances.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"207 ","pages":"Article 105401"},"PeriodicalIF":1.4,"publicationDate":"2024-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143134416","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 : 2024-12-14DOI: 10.1016/j.jmva.2024.105400
Pratim Guha Niyogi , Ping-Shou Zhong
We address the challenge of estimation in the context of constant linear effect models with dense functional responses. In this framework, the conditional expectation of the response curve is represented by a linear combination of functional covariates with constant regression parameters. In this paper, we present an alternative solution by employing the quadratic inference approach, a well-established method for analyzing correlated data, to estimate the regression coefficients. Our approach leverages non-parametrically estimated basis functions, eliminating the need for choosing working correlation structures. Furthermore, we demonstrate that our method achieves a parametric -convergence rate, contingent on an appropriate choice of bandwidth. This convergence is observed when the number of repeated measurements per trajectory exceeds a certain threshold, specifically, when it surpasses , with representing the number of trajectories. Additionally, we establish the asymptotic normality of the resulting estimator. The performance of the proposed method is compared with that of existing methods through extensive simulation studies, where our proposed method outperforms. Real data analysis is also conducted to demonstrate the proposed method.
{"title":"Quadratic inference with dense functional responses","authors":"Pratim Guha Niyogi , Ping-Shou Zhong","doi":"10.1016/j.jmva.2024.105400","DOIUrl":"10.1016/j.jmva.2024.105400","url":null,"abstract":"<div><div>We address the challenge of estimation in the context of constant linear effect models with dense functional responses. In this framework, the conditional expectation of the response curve is represented by a linear combination of functional covariates with constant regression parameters. In this paper, we present an alternative solution by employing the quadratic inference approach, a well-established method for analyzing correlated data, to estimate the regression coefficients. Our approach leverages non-parametrically estimated basis functions, eliminating the need for choosing working correlation structures. Furthermore, we demonstrate that our method achieves a parametric <span><math><msqrt><mrow><mi>n</mi></mrow></msqrt></math></span>-convergence rate, contingent on an appropriate choice of bandwidth. This convergence is observed when the number of repeated measurements per trajectory exceeds a certain threshold, specifically, when it surpasses <span><math><msup><mrow><mi>n</mi></mrow><mrow><msub><mrow><mi>a</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></msup></math></span>, with <span><math><mi>n</mi></math></span> representing the number of trajectories. Additionally, we establish the asymptotic normality of the resulting estimator. The performance of the proposed method is compared with that of existing methods through extensive simulation studies, where our proposed method outperforms. Real data analysis is also conducted to demonstrate the proposed method.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"207 ","pages":"Article 105400"},"PeriodicalIF":1.4,"publicationDate":"2024-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143134411","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 : 2024-12-05DOI: 10.1016/j.jmva.2024.105393
Alexandra Soberon , Massimiliano Mazzanti , Antonio Musolesi , Juan M. Rodriguez-Poo
This paper considers efficiency improvements in a partially linear panel data model that accounts for possible nonlinear effects of common covariates and allows for cross-sectional dependence arising simultaneously from unobserved common factors and spatial dependence. A generalized least squares-type estimator is proposed by taking into account this dependence structure. Also, possible gains in terms of the rate of convergence are studied. A Monte Carlo study is carried out to investigate the proposed estimators’ finite sample performance. Further, an empirical application is conducted to assess the impact of the carbon price linked to the European Union Emission Trading System on carbon dioxide emissions.
{"title":"Efficient estimation of a partially linear panel data model with cross-sectional dependence","authors":"Alexandra Soberon , Massimiliano Mazzanti , Antonio Musolesi , Juan M. Rodriguez-Poo","doi":"10.1016/j.jmva.2024.105393","DOIUrl":"10.1016/j.jmva.2024.105393","url":null,"abstract":"<div><div>This paper considers efficiency improvements in a partially linear panel data model that accounts for possible nonlinear effects of common covariates and allows for cross-sectional dependence arising simultaneously from unobserved common factors and spatial dependence. A generalized least squares-type estimator is proposed by taking into account this dependence structure. Also, possible gains in terms of the rate of convergence are studied. A Monte Carlo study is carried out to investigate the proposed estimators’ finite sample performance. Further, an empirical application is conducted to assess the impact of the carbon price linked to the European Union Emission Trading System on carbon dioxide emissions.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"206 ","pages":"Article 105393"},"PeriodicalIF":1.4,"publicationDate":"2024-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143137999","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 propose an equality test to compare two covariance matrices in a high-dimensional framework while accommodating a low-dimensional latent factor model. We show that null limiting distributions of the test statistics follow a weighted mixture of chi-square distributions under a high-dimensional asymptotic regime combined with weak technical conditions. This distribution depends on the noise covariance matrix and the number of latent factors. Because latent factors are often unknown, we employ an estimation that builds on recent advances in random matrix theory. A numerical study demonstrates the asymptotic power of the proposed test and confirms its favorable analytical properties compared to existing procedures.
{"title":"Equality tests of covariance matrices under a low-dimensional factor structure","authors":"Masashi Hyodo , Takahiro Nishiyama , Hiroki Watanabe , Tomoyuki Nakagawa , Kouji Tahata","doi":"10.1016/j.jmva.2024.105397","DOIUrl":"10.1016/j.jmva.2024.105397","url":null,"abstract":"<div><div>We propose an equality test to compare two covariance matrices in a high-dimensional framework while accommodating a low-dimensional latent factor model. We show that null limiting distributions of the test statistics follow a weighted mixture of chi-square distributions under a high-dimensional asymptotic regime combined with weak technical conditions. This distribution depends on the noise covariance matrix and the number of latent factors. Because latent factors are often unknown, we employ an estimation that builds on recent advances in random matrix theory. A numerical study demonstrates the asymptotic power of the proposed test and confirms its favorable analytical properties compared to existing procedures.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"206 ","pages":"Article 105397"},"PeriodicalIF":1.4,"publicationDate":"2024-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143138000","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 : 2024-11-29DOI: 10.1016/j.jmva.2024.105396
Jakub Woźny , Piotr Jaworski , Damian Jelito , Marcin Pitera , Agnieszka Wyłomańska
We present a novel data-oriented statistical framework that assesses the presumed Gaussian dependence structure in a pairwise setting. This refers to both multivariate normality and normal copula goodness-of-fit testing. The proposed test clusters the data according to the 20/60/20 rule and confronts conditional covariance (or correlation) estimates on the obtained subsets. The corresponding test statistic has a natural practical interpretation, desirable statistical properties, and asymptotic pivotal distribution under the multivariate normality assumption. We illustrate the usefulness of the introduced framework using extensive power simulation studies and show that our approach outperforms popular benchmark alternatives. Also, we apply the proposed methodology to exemplary commodity and equity market data.
{"title":"Gaussian dependence structure pairwise goodness-of-fit testing based on conditional covariance and the 20/60/20 rule","authors":"Jakub Woźny , Piotr Jaworski , Damian Jelito , Marcin Pitera , Agnieszka Wyłomańska","doi":"10.1016/j.jmva.2024.105396","DOIUrl":"10.1016/j.jmva.2024.105396","url":null,"abstract":"<div><div>We present a novel data-oriented statistical framework that assesses the presumed Gaussian dependence structure in a pairwise setting. This refers to both multivariate normality and normal copula goodness-of-fit testing. The proposed test clusters the data according to the 20/60/20 rule and confronts conditional covariance (or correlation) estimates on the obtained subsets. The corresponding test statistic has a natural practical interpretation, desirable statistical properties, and asymptotic pivotal distribution under the multivariate normality assumption. We illustrate the usefulness of the introduced framework using extensive power simulation studies and show that our approach outperforms popular benchmark alternatives. Also, we apply the proposed methodology to exemplary commodity and equity market data.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"206 ","pages":"Article 105396"},"PeriodicalIF":1.4,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143138044","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 : 2024-11-28DOI: 10.1016/j.jmva.2024.105395
Li Ma , Shenghao Qin , Yin Xia
Tensor-valued data arise frequently from a wide variety of scientific applications, and many among them can be translated into an alteration detection problem of tensor dependence structures. In this article, we formulate the problem under the popularly adopted tensor-normal distributions and aim at two-sample correlation/partial correlation comparisons of tensor-valued observations. Through decorrelation and centralization, a separable covariance structure is employed to pool sample information from different tensor modes to enhance the power of the test. Additionally, we propose a novel Sparsity-Exploited Reranking Algorithm (SERA) to further improve the multiple testing efficiency. Such efficiency gain is achieved by incorporating a carefully constructed auxiliary tensor sequence to rerank the -values. Besides the tensor framework, SERA is also generally applicable to a wide range of two-sample large-scale inference problems with sparsity structures, and is of independent interest. The asymptotic properties of the proposed test are derived and the algorithm is shown to control the false discovery at the pre-specified level. We demonstrate the efficacy of the proposed method through intensive simulations and two scientific applications.
{"title":"Alteration detection of tensor dependence structure via sparsity-exploited reranking algorithm","authors":"Li Ma , Shenghao Qin , Yin Xia","doi":"10.1016/j.jmva.2024.105395","DOIUrl":"10.1016/j.jmva.2024.105395","url":null,"abstract":"<div><div>Tensor-valued data arise frequently from a wide variety of scientific applications, and many among them can be translated into an alteration detection problem of tensor dependence structures. In this article, we formulate the problem under the popularly adopted tensor-normal distributions and aim at two-sample correlation/partial correlation comparisons of tensor-valued observations. Through decorrelation and centralization, a separable covariance structure is employed to pool sample information from different tensor modes to enhance the power of the test. Additionally, we propose a novel Sparsity-Exploited Reranking Algorithm (SERA) to further improve the multiple testing efficiency. Such efficiency gain is achieved by incorporating a carefully constructed auxiliary tensor sequence to rerank the <span><math><mi>p</mi></math></span>-values. Besides the tensor framework, SERA is also generally applicable to a wide range of two-sample large-scale inference problems with sparsity structures, and is of independent interest. The asymptotic properties of the proposed test are derived and the algorithm is shown to control the false discovery at the pre-specified level. We demonstrate the efficacy of the proposed method through intensive simulations and two scientific applications.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"206 ","pages":"Article 105395"},"PeriodicalIF":1.4,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143138043","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 : 2024-11-28DOI: 10.1016/j.jmva.2024.105394
Marco Capaldo , Jorge Navarro
The Gini’s mean difference was defined as the expected absolute difference between a random variable and its independent copy. The corresponding normalized version, namely Gini’s index, denotes two times the area between the egalitarian line and the Lorenz curve. Both are dispersion indices because they quantify how far a random variable and its independent copy are. Aiming to measure dispersion in the multivariate case, we define and study new Gini’s indices. For the bivariate case we provide several results and we point out that they are “dependence-dispersion” indices. Covariance representations are exhibited, with an interpretation also in terms of conditional distributions. Further results, bounds and illustrative examples are discussed too. Multivariate extensions are defined, aiming to apply both indices in more general settings. Then, we define efficiency Gini’s indices for any semi-coherent system and we discuss about their interpretation. Empirical versions are considered as well in order to apply multivariate Gini’s indices to data.
{"title":"New multivariate Gini’s indices","authors":"Marco Capaldo , Jorge Navarro","doi":"10.1016/j.jmva.2024.105394","DOIUrl":"10.1016/j.jmva.2024.105394","url":null,"abstract":"<div><div>The Gini’s mean difference was defined as the expected absolute difference between a random variable and its independent copy. The corresponding normalized version, namely Gini’s index, denotes two times the area between the egalitarian line and the Lorenz curve. Both are dispersion indices because they quantify how far a random variable and its independent copy are. Aiming to measure dispersion in the multivariate case, we define and study new Gini’s indices. For the bivariate case we provide several results and we point out that they are “dependence-dispersion” indices. Covariance representations are exhibited, with an interpretation also in terms of conditional distributions. Further results, bounds and illustrative examples are discussed too. Multivariate extensions are defined, aiming to apply both indices in more general settings. Then, we define efficiency Gini’s indices for any semi-coherent system and we discuss about their interpretation. Empirical versions are considered as well in order to apply multivariate Gini’s indices to data.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"206 ","pages":"Article 105394"},"PeriodicalIF":1.4,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143137983","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-26DOI: 10.1016/j.jmva.2024.105392
Keunbaik Lee , Jongwoo Choi , Eun Jin Jang , Dipak Dey
Linear models commonly used in longitudinal data analysis often assume a multivariate normal distribution. This assumption, however, can lead to biased mean parameter estimates in the presence of outliers. To address this, alternative linear models based on multivariate t distributions have been developed. In this paper, we review the commonly used multivariate distributions applicable to multivariate longitudinal data and introduce multivariate Laplace linear models (MLLMs) that are designed to handle outliers effectively. These models incorporate a scale matrix that is autoregressive, heteroscedastic, and positive definite, using modified Cholesky and hypersphere decompositions. We conduct simulation studies and apply these models to a real data example, comparing the performance of MLLMs with multivariate normal linear models (MNLMs) and multivariate t linear models (MTLMs), and providing insights on when each model is most appropriate.
{"title":"Multivariate robust linear models for multivariate longitudinal data","authors":"Keunbaik Lee , Jongwoo Choi , Eun Jin Jang , Dipak Dey","doi":"10.1016/j.jmva.2024.105392","DOIUrl":"10.1016/j.jmva.2024.105392","url":null,"abstract":"<div><div>Linear models commonly used in longitudinal data analysis often assume a multivariate normal distribution. This assumption, however, can lead to biased mean parameter estimates in the presence of outliers. To address this, alternative linear models based on multivariate t distributions have been developed. In this paper, we review the commonly used multivariate distributions applicable to multivariate longitudinal data and introduce multivariate Laplace linear models (MLLMs) that are designed to handle outliers effectively. These models incorporate a scale matrix that is autoregressive, heteroscedastic, and positive definite, using modified Cholesky and hypersphere decompositions. We conduct simulation studies and apply these models to a real data example, comparing the performance of MLLMs with multivariate normal linear models (MNLMs) and multivariate t linear models (MTLMs), and providing insights on when each model is most appropriate.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"206 ","pages":"Article 105392"},"PeriodicalIF":1.4,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142744156","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 : 2024-11-16DOI: 10.1016/j.jmva.2024.105384
Daniel Gaigall , Shunyao Wu , Hua Liang
We generalize the projection correlation idea for testing independence of random vectors which is known as a powerful method in multivariate analysis. A universal Hilbert space approach makes the new testing procedures useful in various cases and ensures the applicability to high or even infinite dimensional data. We prove that the new tests keep the significance level under the null hypothesis of independence exactly and can detect any alternative of dependence in the limit, in particular in settings where the dimensions of the observations is infinite or tend to infinity simultaneously with the sample size. Simulations demonstrate that the generalization does not impair the good performance of the approach and confirm our theoretical findings. Furthermore, we describe the implementation of the new approach and present a real data example for illustration.
{"title":"A general approach for testing independence in Hilbert spaces","authors":"Daniel Gaigall , Shunyao Wu , Hua Liang","doi":"10.1016/j.jmva.2024.105384","DOIUrl":"10.1016/j.jmva.2024.105384","url":null,"abstract":"<div><div>We generalize the projection correlation idea for testing independence of random vectors which is known as a powerful method in multivariate analysis. A universal Hilbert space approach makes the new testing procedures useful in various cases and ensures the applicability to high or even infinite dimensional data. We prove that the new tests keep the significance level under the null hypothesis of independence exactly and can detect any alternative of dependence in the limit, in particular in settings where the dimensions of the observations is infinite or tend to infinity simultaneously with the sample size. Simulations demonstrate that the generalization does not impair the good performance of the approach and confirm our theoretical findings. Furthermore, we describe the implementation of the new approach and present a real data example for illustration.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"206 ","pages":"Article 105384"},"PeriodicalIF":1.4,"publicationDate":"2024-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142723652","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-15DOI: 10.1016/j.jmva.2024.105383
Qingzhi Zhong , Xinyuan Song
The functional varying-coefficient model (FVCM) provides a simple yet efficient method for function on scalar regression. However, classical FVCM typically assumes that varying associations between functional responses and scalar covariates are identical for all subjects and nonzero in the entire domain of functional measures. This study considers sparse functional varying-coefficient mixture regression, which allows heterogeneous regression associations and dependency structure among multiple functional responses and accommodates functional sparsity in varying coefficient functions. Moreover, we devise a computationally efficient EM algorithm with a double-sparse penalty for estimation. We show that the proposed estimator is consistent, can uncover sparse subregions, and simultaneously select the number of clusters with probability tending to one. Simulation studies and an application to the Alzheimer’s Disease Neuroimaging Initiative study confirm that the proposed method yields more interpretable results and a much lower classification error than existing methods.
功能变化系数模型（FVCM）为标量回归函数提供了一种简单而有效的方法。然而，经典的 FVCM 通常假定所有受试者的功能反应和标量协变量之间的变化关联是相同的，并且在整个功能测量域中都不为零。本研究考虑了稀疏功能变化系数混合回归，它允许多种功能反应之间存在异质回归关联和依赖结构，并适应变化系数函数中的功能稀疏性。此外，我们还设计了一种计算高效的 EM 算法，采用双稀疏惩罚进行估计。我们证明了所提出的估计方法是一致的，可以发现稀疏的子区域，并同时以趋近于 1 的概率选择簇的数量。模拟研究和阿尔茨海默病神经成像计划研究的应用证实，与现有方法相比，所提出的方法能产生更多可解释的结果，分类误差也更小。
{"title":"Sparse functional varying-coefficient mixture regression","authors":"Qingzhi Zhong , Xinyuan Song","doi":"10.1016/j.jmva.2024.105383","DOIUrl":"10.1016/j.jmva.2024.105383","url":null,"abstract":"<div><div>The functional varying-coefficient model (FVCM) provides a simple yet efficient method for function on scalar regression. However, classical FVCM typically assumes that varying associations between functional responses and scalar covariates are identical for all subjects and nonzero in the entire domain of functional measures. This study considers sparse functional varying-coefficient mixture regression, which allows heterogeneous regression associations and dependency structure among multiple functional responses and accommodates functional sparsity in varying coefficient functions. Moreover, we devise a computationally efficient EM algorithm with a double-sparse penalty for estimation. We show that the proposed estimator is consistent, can uncover sparse subregions, and simultaneously select the number of clusters with probability tending to one. Simulation studies and an application to the Alzheimer’s Disease Neuroimaging Initiative study confirm that the proposed method yields more interpretable results and a much lower classification error than existing methods.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"206 ","pages":"Article 105383"},"PeriodicalIF":1.4,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142704784","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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