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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
Explicit bivariate simplicial depth 显式二维简单深度
IF 1.4 3区 数学
Journal of Multivariate Analysis Pub Date : 2024-09-30 DOI: 10.1016/j.jmva.2024.105375
Erik Mendroš, Stanislav Nagy
{"title":"Explicit bivariate simplicial depth","authors":"Erik Mendroš,&nbsp;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}
引用次数: 0
Large sample correlation matrices with unbounded spectrum 具有无界频谱的大样本相关矩阵
IF 1.4 3区 数学
Journal of Multivariate Analysis Pub Date : 2024-09-27 DOI: 10.1016/j.jmva.2024.105373
Yanpeng Li
{"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}
引用次数: 0
Detection and localization of changes in a panel of densities 密度面板变化的检测和定位
IF 1.4 3区 数学
Journal of Multivariate Analysis Pub Date : 2024-09-24 DOI: 10.1016/j.jmva.2024.105374
Tim Kutta , Agnieszka Jach , Michel Ferreira Cardia Haddad , Piotr Kokoszka , Haonan Wang
{"title":"Detection and localization of changes in a panel of densities","authors":"Tim Kutta ,&nbsp;Agnieszka Jach ,&nbsp;Michel Ferreira Cardia Haddad ,&nbsp;Piotr Kokoszka ,&nbsp;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}
引用次数: 0
Data depth functions for non-standard data by use of formal concept analysis 利用形式概念分析实现非标准数据的数据深度函数
IF 1.4 3区 数学
Journal of Multivariate Analysis Pub Date : 2024-09-19 DOI: 10.1016/j.jmva.2024.105372
Hannah Blocher, Georg Schollmeyer
{"title":"Data depth functions for non-standard data by use of formal concept analysis","authors":"Hannah Blocher,&nbsp;Georg Schollmeyer","doi":"10.1016/j.jmva.2024.105372","DOIUrl":"10.1016/j.jmva.2024.105372","url":null,"abstract":"<div><div>In this article we introduce a notion of depth functions for data types that are not given in standard statistical data formats. We focus on data that cannot be represented by one specific data structure, such as normed vector spaces. This covers a wide range of different data types, which we refer to as non-standard data. Depth functions have been studied intensively for normed vector spaces. However, a discussion of depth functions for non-standard data is lacking. In this article, we address this gap by using formal concept analysis to obtain a unified data representation. Building on this representation, we then define depth functions for non-standard data. Furthermore, we provide a systematic basis by introducing structural properties using the data representation provided by formal concept analysis. Finally, we embed the generalised Tukey depth into our concept of data depth and analyse it using the introduced structural properties. Thus, this article presents the mathematical formalisation of centrality and outlyingness for non-standard data and increases the number of spaces in which centrality can be discussed. In particular, we provide a basis for defining further depth functions and statistical inference methods for non-standard data.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"205 ","pages":"Article 105372"},"PeriodicalIF":1.4,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142327125","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
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