Pub Date : 2024-11-10DOI: 10.1016/j.jmva.2024.105382
Moosup Kim , Sangyeol Lee
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.
{"title":"Maximum likelihood estimation of elliptical tail","authors":"Moosup Kim , 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}
Pub Date : 2024-10-28DOI: 10.1016/j.jmva.2024.105380
Lucas Reding , Andrés F. López-Lopera , François Bachoc
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.
{"title":"Covariance parameter estimation of Gaussian processes with approximated functional inputs","authors":"Lucas Reding , Andrés F. López-Lopera , 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}
Pub Date : 2024-10-24DOI: 10.1016/j.jmva.2024.105381
Cristian Castiglione , Eleonora Arnone , Mauro Bernardi , Alessio Farcomeni , Laura M. Sangalli
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.
{"title":"PDE-regularised spatial quantile regression","authors":"Cristian Castiglione , Eleonora Arnone , Mauro Bernardi , Alessio Farcomeni , 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}
Pub Date : 2024-10-17DOI: 10.1016/j.jmva.2024.105379
Yacouba Boubacar Maïnassara , Eugen Ursu
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.
{"title":"Diagnostic checking of periodic vector autoregressive time series models with dependent errors","authors":"Yacouba Boubacar Maïnassara , 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}
Pub Date : 2024-10-11DOI: 10.1016/j.jmva.2024.105378
Li Wang , Hongyi Zhou , Weidong Ma , Ying Yang
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 categories, we propose slicing estimators to estimate our index. We conduct an asymptotic analysis for the slicing estimators, considering both situations where is fixed and where 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.
我们引入了一种新的指数来衡量两个随机向量之间的依赖程度并检验其独立性。该指数是通过投影平均技术对条件分布函数和边际分布函数之间的 Cramér-von Mises 距离进行一般化而得到的。如果其中一个随机向量是有 K 个类别的分类向量，我们将提出切片估计器来估计我们的指数。我们对切分估计器进行了渐近分析，考虑了 K 固定和允许 K 随样本量增加的两种情况。当两个随机向量都是连续的时候，我们为提出的指数引入了核回归估计器，证明其渐近零分布遵循正态分布，并对基于核估计器的独立性检验进行了局部幂次分析。我们通过模拟对所提出的检验进行了研究，并提供了一个真实数据应用来说明我们的方法。
{"title":"A conditional distribution function-based measure for independence and K-sample tests in multivariate data","authors":"Li Wang , Hongyi Zhou , Weidong Ma , 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}
Pub Date : 2024-10-09DOI: 10.1016/j.jmva.2024.105377
Marco Tschimpke
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 and Blest’s measure of rank correlation for bivariate extreme-value copulas (EVCs). Moreover, in the well-studied class of EVCs, exact regions for Spearman’s footrule /Blomqvist’s and Spearman’s , Kendall’s or Blest’s symmetrised measure of rank correlation are provided. A performance analysis comparing rank-based estimators of and with estimators using that the sample is drawn from an extreme-value copula concludes this paper.
{"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}
Pub Date : 2024-10-05DOI: 10.1016/j.jmva.2024.105376
Olha Bodnar , Taras Bodnar
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.
{"title":"Birge ratio method for modeling dark uncertainty in multivariate meta-analyses and inter-laboratory studies","authors":"Olha Bodnar , 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}
Pub Date : 2024-09-30DOI: 10.1016/j.jmva.2024.105375
Erik Mendroš, Stanislav Nagy
The simplicial depth (SD) is a celebrated tool defining elements of nonparametric and robust statistics for multivariate data. While many properties of SD are well-established, and its applications are abundant, explicit expressions for SD are known only for a handful of the simplest multivariate probability distributions. This paper deals with SD in the plane. It (i) develops a one-dimensional integral formula for SD of any properly continuous probability distribution, (ii) gives exact explicit expressions for SD of uniform distributions on (both convex and non-convex) polygons in the plane or on the boundaries of such polygons, and (iii) discusses several implications of these findings to probability and statistics: (a) An upper bound on the maximum SD in the plane, (b) an implication for a test of symmetry of a bivariate distribution, and (c) a connection of SD with the classical Sylvester problem from geometric probability.
{"title":"Explicit bivariate simplicial depth","authors":"Erik Mendroš, Stanislav Nagy","doi":"10.1016/j.jmva.2024.105375","DOIUrl":"10.1016/j.jmva.2024.105375","url":null,"abstract":"<div><div>The simplicial depth (SD) is a celebrated tool defining elements of nonparametric and robust statistics for multivariate data. While many properties of SD are well-established, and its applications are abundant, explicit expressions for SD are known only for a handful of the simplest multivariate probability distributions. This paper deals with SD in the plane. It (i) develops a one-dimensional integral formula for SD of any properly continuous probability distribution, (ii) gives exact explicit expressions for SD of uniform distributions on (both convex and non-convex) polygons in the plane or on the boundaries of such polygons, and (iii) discusses several implications of these findings to probability and statistics: (a) An upper bound on the maximum SD in the plane, (b) an implication for a test of symmetry of a bivariate distribution, and (c) a connection of SD with the classical Sylvester problem from geometric probability.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"205 ","pages":"Article 105375"},"PeriodicalIF":1.4,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142428480","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 : 2024-09-27DOI: 10.1016/j.jmva.2024.105373
Yanpeng Li
In this paper, we demonstrate that the diagonal of a high-dimensional sample covariance matrix stemming from independent observations of a -dimensional time series with finite fourth moments can be approximated in spectral norm by the diagonal of the population covariance matrix regardless of the spectral norm of the population covariance matrix. Our assumptions involve and tending to infinity, with tending to a constant which might be positive or zero. Consequently, we investigate the asymptotic properties of the sample correlation matrix with a divergent spectrum, and we explore its applications by deriving the limiting spectral distribution for its eigenvalues and analyzing the convergence of divergent and non-divergent spiked eigenvalues under a generalized spiked correlation framework.
在本文中，我们证明了由具有有限第四矩的 p 维时间序列的 n 个独立观测值所产生的高维样本协方差矩阵的对角线，在谱规范上可以用总体协方差矩阵的对角线来近似，而与总体协方差矩阵的谱规范无关。我们的假设是 p 和 n 趋于无穷大，p/n 趋于一个常数，这个常数可能是正数，也可能是零。因此，我们研究了具有发散谱的样本相关矩阵的渐近特性，并通过推导其特征值的极限谱分布以及分析广义尖峰相关框架下发散和非发散尖峰特征值的收敛性，探索了其应用。
{"title":"Large sample correlation matrices with unbounded spectrum","authors":"Yanpeng Li","doi":"10.1016/j.jmva.2024.105373","DOIUrl":"10.1016/j.jmva.2024.105373","url":null,"abstract":"<div><div>In this paper, we demonstrate that the diagonal of a high-dimensional sample covariance matrix stemming from <span><math><mi>n</mi></math></span> independent observations of a <span><math><mi>p</mi></math></span>-dimensional time series with finite fourth moments can be approximated in spectral norm by the diagonal of the population covariance matrix regardless of the spectral norm of the population covariance matrix. Our assumptions involve <span><math><mi>p</mi></math></span> and <span><math><mi>n</mi></math></span> tending to infinity, with <span><math><mrow><mi>p</mi><mo>/</mo><mi>n</mi></mrow></math></span> tending to a constant which might be positive or zero. Consequently, we investigate the asymptotic properties of the sample correlation matrix with a divergent spectrum, and we explore its applications by deriving the limiting spectral distribution for its eigenvalues and analyzing the convergence of divergent and non-divergent spiked eigenvalues under a generalized spiked correlation framework.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"205 ","pages":"Article 105373"},"PeriodicalIF":1.4,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142428479","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 : 2024-09-24DOI: 10.1016/j.jmva.2024.105374
Tim Kutta , Agnieszka Jach , Michel Ferreira Cardia Haddad , Piotr Kokoszka , Haonan Wang
We propose a new methodology for identifying and localizing changes in the Fréchet mean of a multivariate time series of probability densities. The functional data objects we study are random densities indexed by discrete time and a vector component , which can be treated as a broadly understood spatial location. Our main objective is to identify the set of components , where a change occurs with statistical certainty. A challenge of this analysis is that the densities are not directly observable and must be estimated from sparse and potentially imbalanced data. Such setups are motivated by the analysis of two data sets that we investigate in this work. First, a hitherto unpublished large data set of Brazilian Covid infections and a second, a financial data set derived from intraday prices of U.S. Exchange Traded Funds. Chief statistical advances are the development of change point tests and estimators of components of change for multivariate time series of densities. We prove the theoretical validity of our methodology and investigate its finite sample performance in a simulation study.
我们提出了一种新方法，用于识别和定位概率密度多元时间序列的弗雷谢特均值变化。我们研究的功能数据对象是以离散时间 t 和矢量分量 s 为索引的随机密度 fs,t，后者可视为广义上的空间位置。我们的主要目标是找出在统计上确定发生变化的分量 s 的集合。这项分析的挑战在于，密度 fs,t 无法直接观测，必须从稀疏且可能不平衡的数据中估算出来。我们在本研究中对两组数据进行了分析，从而激发了这种设置。第一组是迄今为止尚未发表的巴西 Covid 感染的大型数据集，第二组是源自美国交易所交易基金盘中价格的金融数据集。统计方面的主要进展是开发了变化点检验和多元时间序列密度变化成分估计器。我们证明了我们方法的理论有效性，并在模拟研究中调查了其有限样本性能。
{"title":"Detection and localization of changes in a panel of densities","authors":"Tim Kutta , Agnieszka Jach , Michel Ferreira Cardia Haddad , Piotr Kokoszka , Haonan Wang","doi":"10.1016/j.jmva.2024.105374","DOIUrl":"10.1016/j.jmva.2024.105374","url":null,"abstract":"<div><div>We propose a new methodology for identifying and localizing changes in the Fréchet mean of a multivariate time series of probability densities. The functional data objects we study are random densities <span><math><msub><mrow><mi>f</mi></mrow><mrow><mi>s</mi><mo>,</mo><mi>t</mi></mrow></msub></math></span> indexed by discrete time <span><math><mi>t</mi></math></span> and a vector component <span><math><mi>s</mi></math></span>, which can be treated as a broadly understood spatial location. Our main objective is to identify the set of components <span><math><mi>s</mi></math></span>, where a change occurs with statistical certainty. A challenge of this analysis is that the densities <span><math><msub><mrow><mi>f</mi></mrow><mrow><mi>s</mi><mo>,</mo><mi>t</mi></mrow></msub></math></span> are not directly observable and must be estimated from sparse and potentially imbalanced data. Such setups are motivated by the analysis of two data sets that we investigate in this work. First, a hitherto unpublished large data set of Brazilian Covid infections and a second, a financial data set derived from intraday prices of U.S. Exchange Traded Funds. Chief statistical advances are the development of change point tests and estimators of components of change for multivariate time series of densities. We prove the theoretical validity of our methodology and investigate its finite sample performance in a simulation study.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"205 ","pages":"Article 105374"},"PeriodicalIF":1.4,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142327131","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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