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Multivariate robust linear models for multivariate longitudinal data
IF 1.4 3区 数学
Journal of Multivariate Analysis Pub Date : 2024-11-26 DOI: 10.1016/j.jmva.2024.105392
Keunbaik Lee , Jongwoo Choi , Eun Jin Jang , Dipak Dey
{"title":"Multivariate robust linear models for multivariate longitudinal data","authors":"Keunbaik Lee ,&nbsp;Jongwoo Choi ,&nbsp;Eun Jin Jang ,&nbsp;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}
引用次数: 0
A general approach for testing independence in Hilbert spaces 检验希尔伯特空间独立性的一般方法
IF 1.4 3区 数学
Journal of Multivariate Analysis Pub Date : 2024-11-16 DOI: 10.1016/j.jmva.2024.105384
Daniel Gaigall , Shunyao Wu , Hua Liang
{"title":"A general approach for testing independence in Hilbert spaces","authors":"Daniel Gaigall ,&nbsp;Shunyao Wu ,&nbsp;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}
引用次数: 0
Sparse functional varying-coefficient mixture regression 稀疏函数变化系数混合回归
IF 1.4 3区 数学
Journal of Multivariate Analysis Pub Date : 2024-11-15 DOI: 10.1016/j.jmva.2024.105383
Qingzhi Zhong , Xinyuan Song
{"title":"Sparse functional varying-coefficient mixture regression","authors":"Qingzhi Zhong ,&nbsp;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}
引用次数: 0
Maximum likelihood estimation of elliptical tail 椭圆尾部的最大似然估计
IF 1.4 3区 数学
Journal of Multivariate Analysis Pub Date : 2024-11-10 DOI: 10.1016/j.jmva.2024.105382
Moosup Kim , Sangyeol Lee
{"title":"Maximum likelihood estimation of elliptical tail","authors":"Moosup Kim ,&nbsp;Sangyeol Lee","doi":"10.1016/j.jmva.2024.105382","DOIUrl":"10.1016/j.jmva.2024.105382","url":null,"abstract":"<div><div>This study is focused on the efficient estimation of the elliptical tail. Initially, we derive the density function of the spectral measure of an elliptical distribution concerning a dominating measure on the unit sphere, which consequently leads to the density function of the elliptical tail. Subsequently, we propose a maximum likelihood estimation based on the derived density function class. The resulting maximum likelihood estimator (MLE) is proven to be consistent and asymptotically normal. Moreover, it is demonstrated that the MLE is asymptotically efficient, with the added advantage that its asymptotic covariance matrix can be feasibly estimated at a low computational cost. A simulation study and real data analysis are conducted to illustrate the efficacy of the proposed method.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"205 ","pages":"Article 105382"},"PeriodicalIF":1.4,"publicationDate":"2024-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142658552","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}
引用次数: 0
Covariance parameter estimation of Gaussian processes with approximated functional inputs 具有近似函数输入的高斯过程的协方差参数估计
IF 1.4 3区 数学
Journal of Multivariate Analysis Pub Date : 2024-10-28 DOI: 10.1016/j.jmva.2024.105380
Lucas Reding , Andrés F. López-Lopera , François Bachoc
{"title":"Covariance parameter estimation of Gaussian processes with approximated functional inputs","authors":"Lucas Reding ,&nbsp;Andrés F. López-Lopera ,&nbsp;François Bachoc","doi":"10.1016/j.jmva.2024.105380","DOIUrl":"10.1016/j.jmva.2024.105380","url":null,"abstract":"<div><div>We consider the problem of covariance parameter estimation for Gaussian processes with functional inputs. Our study addresses scenarios where exact functional inputs are available and where only approximate versions of these functions are accessible. From an increasing-domain asymptotics perspective, we first establish the asymptotic consistency and normality of the maximum likelihood estimator for the exact inputs. Then, by accounting for approximation errors, we certify the robustness of practical implementations that rely on conventional sampling methods or projections onto a functional basis. Loosely speaking, both consistency and normality continue to hold when the approximation error becomes negligible, a condition often met as the number of samples or basis functions becomes large. To ensure broad applicability, our asymptotic analysis is conducted for any Hilbert space of inputs. Our findings are illustrated through analytical examples, including the case of non-randomly perturbed grids, as well as several numerical illustrations.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"205 ","pages":"Article 105380"},"PeriodicalIF":1.4,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142592553","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}
引用次数: 0
PDE-regularised spatial quantile regression PDE 规则化空间量化回归
IF 1.4 3区 数学
Journal of Multivariate Analysis Pub Date : 2024-10-24 DOI: 10.1016/j.jmva.2024.105381
Cristian Castiglione , Eleonora Arnone , Mauro Bernardi , Alessio Farcomeni , Laura M. Sangalli
{"title":"PDE-regularised spatial quantile regression","authors":"Cristian Castiglione ,&nbsp;Eleonora Arnone ,&nbsp;Mauro Bernardi ,&nbsp;Alessio Farcomeni ,&nbsp;Laura M. Sangalli","doi":"10.1016/j.jmva.2024.105381","DOIUrl":"10.1016/j.jmva.2024.105381","url":null,"abstract":"<div><div>We consider the problem of estimating the conditional quantiles of an unknown distribution from data gathered on a spatial domain. We propose a spatial quantile regression model with differential regularisation. The penalisation involves a partial differential equation defined over the considered spatial domain, that can display a complex geometry. Such regularisation permits, on one hand, to model complex anisotropy and non-stationarity patterns, possibly on the basis of problem-specific knowledge, and, on the other hand, to comply with the complex conformation of the spatial domain. We define an innovative functional Expectation–Maximisation algorithm, to estimate the unknown quantile surface. We moreover describe a suitable discretisation of the estimation problem, and investigate the theoretical properties of the resulting estimator. The performance of the proposed method is assessed by simulation studies, comparing with state-of-the-art techniques for spatial quantile regression. Finally, the considered model is applied to two real data analyses, the first concerning rainfall measurements in Switzerland and the second concerning sea surface conductivity data in the Gulf of Mexico.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"205 ","pages":"Article 105381"},"PeriodicalIF":1.4,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142572576","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}
引用次数: 0
Diagnostic checking of periodic vector autoregressive time series models with dependent errors 有依赖误差的周期向量自回归时间序列模型的诊断检查
IF 1.4 3区 数学
Journal of Multivariate Analysis Pub Date : 2024-10-17 DOI: 10.1016/j.jmva.2024.105379
Yacouba Boubacar Maïnassara , Eugen Ursu
{"title":"Diagnostic checking of periodic vector autoregressive time series models with dependent errors","authors":"Yacouba Boubacar Maïnassara ,&nbsp;Eugen Ursu","doi":"10.1016/j.jmva.2024.105379","DOIUrl":"10.1016/j.jmva.2024.105379","url":null,"abstract":"<div><div>In this article, we study the asymptotic behavior of the residual autocorrelations for periodic vector autoregressive time series models (PVAR henceforth) with uncorrelated but dependent innovations (i.e., weak PVAR). We then deduce the asymptotic distribution of the Ljung–Box-McLeod modified Portmanteau statistics for weak PVAR models. In Monte Carlo experiments, we illustrate that the proposed test statistics have reasonable finite sample performance. When the innovations exhibit conditional heteroscedasticity or other forms of dependence, it appears that the standard test statistics (under independent and identically distributed innovations) are generally unreliable, overrejecting, or underrejecting severely, while the proposed test statistics offer satisfactory levels. The proposed methodology is employed in the analysis of two river flows.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"205 ","pages":"Article 105379"},"PeriodicalIF":1.4,"publicationDate":"2024-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142531333","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}
引用次数: 0
A conditional distribution function-based measure for independence and K-sample tests in multivariate data 基于条件分布函数的多元数据独立性和 K 样本检验测量方法
IF 1.4 3区 数学
Journal of Multivariate Analysis Pub Date : 2024-10-11 DOI: 10.1016/j.jmva.2024.105378
Li Wang , Hongyi Zhou , Weidong Ma , Ying Yang
{"title":"A conditional distribution function-based measure for independence and K-sample tests in multivariate data","authors":"Li Wang ,&nbsp;Hongyi Zhou ,&nbsp;Weidong Ma ,&nbsp;Ying Yang","doi":"10.1016/j.jmva.2024.105378","DOIUrl":"10.1016/j.jmva.2024.105378","url":null,"abstract":"<div><div>We introduce a new index to measure the degree of dependence and test for independence between two random vectors. The index is obtained by generalizing the Cramér–von Mises distances between the conditional and marginal distribution functions via the projection-averaging technique. If one of the random vectors is categorical with <span><math><mi>K</mi></math></span> categories, we propose slicing estimators to estimate our index. We conduct an asymptotic analysis for the slicing estimators, considering both situations where <span><math><mi>K</mi></math></span> is fixed and where <span><math><mi>K</mi></math></span> is allowed to increase with the sample size. When both random vectors are continuous, we introduce a kernel regression estimator for the proposed index, demonstrating that its asymptotic null distribution follows a normal distribution and conducting a local power analysis for the kernel estimator-based independence test. The proposed tests are studied via simulations, with a real data application presented to illustrate our methods.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"205 ","pages":"Article 105378"},"PeriodicalIF":1.4,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142531332","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}
引用次数: 0
On the exact region determined by Spearman’s ρ and Blest’s measure of rank correlation ν for bivariate extreme-value copulas 关于斯皮尔曼ρ和布莱斯特等级相关性ν对二元极值共存关系的测量所确定的确切区域
IF 1.4 3区 数学
Journal of Multivariate Analysis Pub Date : 2024-10-09 DOI: 10.1016/j.jmva.2024.105377
Marco Tschimpke
{"title":"On the exact region determined by Spearman’s ρ and Blest’s measure of rank correlation ν for bivariate extreme-value copulas","authors":"Marco Tschimpke","doi":"10.1016/j.jmva.2024.105377","DOIUrl":"10.1016/j.jmva.2024.105377","url":null,"abstract":"<div><div>Considering pairs of measures of association it has been of interest how much the values of one measure varies, fixing the value of the other one. Motivated by this fact, we establish sharp lower and upper bounds for the region determined by Spearman’s <span><math><mi>ρ</mi></math></span> and Blest’s measure of rank correlation <span><math><mi>ν</mi></math></span> for bivariate extreme-value copulas (EVCs). Moreover, in the well-studied class of EVCs, exact regions for Spearman’s footrule <span><math><mi>ϕ</mi></math></span>/Blomqvist’s <span><math><mi>β</mi></math></span> and Spearman’s <span><math><mi>ρ</mi></math></span>, Kendall’s <span><math><mi>τ</mi></math></span> or Blest’s symmetrised measure of rank correlation <span><math><mi>ξ</mi></math></span> are provided. A performance analysis comparing rank-based estimators of <span><math><mi>ρ</mi></math></span> and <span><math><mi>ν</mi></math></span> with estimators using that the sample is drawn from an extreme-value copula concludes this paper.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"205 ","pages":"Article 105377"},"PeriodicalIF":1.4,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142428482","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}
引用次数: 0
Birge ratio method for modeling dark uncertainty in multivariate meta-analyses and inter-laboratory studies 用于多元荟萃分析和实验室间研究中暗不确定性建模的比尔吉比率法
IF 1.4 3区 数学
Journal of Multivariate Analysis Pub Date : 2024-10-05 DOI: 10.1016/j.jmva.2024.105376
Olha Bodnar , Taras Bodnar
{"title":"Birge ratio method for modeling dark uncertainty in multivariate meta-analyses and inter-laboratory studies","authors":"Olha Bodnar ,&nbsp;Taras Bodnar","doi":"10.1016/j.jmva.2024.105376","DOIUrl":"10.1016/j.jmva.2024.105376","url":null,"abstract":"<div><div>In the paper, we introduce a new approach for combining multivariate measurements obtained in individual studies. The procedure extends the Birge ratio method, a commonly used approach in physics in the univariate case, such as for the determination of physical constants, to multivariate observations. Statistical inference procedures are derived for the parameters of the multivariate location-scale model, which is related to the multivariate Birge ratio method. The new approach provides an alternative to the methods based on the application of the multivariate random effects model, which is commonly used for multivariate meta-analyses and inter-laboratory comparisons. In two empirical illustrations, we show that the introduced multivariate Birge ratio approach yields confidence intervals for the elements of the overall mean vector that are considerably narrower than those obtained by the methods derived under the multivariate random effects model.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"205 ","pages":"Article 105376"},"PeriodicalIF":1.4,"publicationDate":"2024-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142428481","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}
引用次数: 0
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