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Sequential estimation of high-dimensional signal plus noise models under general elliptical frameworks 一般椭圆框架下高维信号加噪声模型的序贯估计
IF 1.4 3区 数学
Journal of Multivariate Analysis Pub Date : 2024-12-30 DOI: 10.1016/j.jmva.2024.105403
Li Yanpeng , Xie Jiahui , Zhou Guoliang , Zhou Wang
{"title":"Sequential estimation of high-dimensional signal plus noise models under general elliptical frameworks","authors":"Li Yanpeng ,&nbsp;Xie Jiahui ,&nbsp;Zhou Guoliang ,&nbsp;Zhou Wang","doi":"10.1016/j.jmva.2024.105403","DOIUrl":"10.1016/j.jmva.2024.105403","url":null,"abstract":"<div><div>High dimensional data analysis has attracted considerable interest and is facing new challenges, one of which is the increasingly available data with noise corrupted and in a streaming manner, such as signals and stocks. In this paper, we develop a sequential method to dynamically update the estimates of signal and noise strength in signal plus noise models. The proposed sequential method is easy to compute based on the stored statistics and the current data point. The consistency and, more importantly, the asymptotic normality of the estimators of signal strength and noise level are demonstrated for high dimensional settings under mild conditions. Simulations and real data examples are further provided to illustrate the practical utility of our proposal.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"207 ","pages":"Article 105403"},"PeriodicalIF":1.4,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143134413","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
Quadratic inference with dense functional responses 具有密集泛函响应的二次推理
IF 1.4 3区 数学
Journal of Multivariate Analysis Pub Date : 2024-12-14 DOI: 10.1016/j.jmva.2024.105400
Pratim Guha Niyogi , Ping-Shou Zhong
{"title":"Quadratic inference with dense functional responses","authors":"Pratim Guha Niyogi ,&nbsp;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}
引用次数: 0
Asymptotics for non-degenerate multivariate U-statistics with estimated nuisance parameters under the null and local alternative hypotheses 非退化多元u统计量在零假设和局部备择假设下的渐近性
IF 1.4 3区 数学
Journal of Multivariate Analysis Pub Date : 2024-12-06 DOI: 10.1016/j.jmva.2024.105398
Alain Desgagné , Christian Genest , Frédéric Ouimet
{"title":"Asymptotics for non-degenerate multivariate U-statistics with estimated nuisance parameters under the null and local alternative hypotheses","authors":"Alain Desgagné ,&nbsp;Christian Genest ,&nbsp;Frédéric Ouimet","doi":"10.1016/j.jmva.2024.105398","DOIUrl":"10.1016/j.jmva.2024.105398","url":null,"abstract":"<div><div>The large-sample behavior of non-degenerate multivariate <span><math><mi>U</mi></math></span>-statistics of arbitrary degree is investigated under the assumption that their kernel depends on parameters that can be estimated consistently. Mild regularity conditions are provided which guarantee that once properly normalized, such statistics are asymptotically multivariate Gaussian both under the null hypothesis and sequences of local alternatives. The work of Randles (1982, <em>Ann. Statist.</em>) is extended in three ways: the data and the kernel values can be multivariate rather than univariate, the limiting behavior under local alternatives is studied for the first time, and the effect of knowing some of the nuisance parameters is quantified. These results can be applied to a broad range of goodness-of-fit testing contexts, as shown in two specific examples.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"208 ","pages":"Article 105398"},"PeriodicalIF":1.4,"publicationDate":"2024-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144500907","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
Efficient estimation of a partially linear panel data model with cross-sectional dependence 具有截面相关性的部分线性面板数据模型的有效估计
IF 1.4 3区 数学
Journal of Multivariate Analysis Pub Date : 2024-12-05 DOI: 10.1016/j.jmva.2024.105393
Alexandra Soberon , Massimiliano Mazzanti , Antonio Musolesi , Juan M. Rodriguez-Poo
{"title":"Efficient estimation of a partially linear panel data model with cross-sectional dependence","authors":"Alexandra Soberon ,&nbsp;Massimiliano Mazzanti ,&nbsp;Antonio Musolesi ,&nbsp;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}
引用次数: 0
Gaussian dependence structure pairwise goodness-of-fit testing based on conditional covariance and the 20/60/20 rule 基于条件协方差和20/60/20规则的高斯依赖结构配对拟合优度检验
IF 1.4 3区 数学
Journal of Multivariate Analysis Pub Date : 2024-11-29 DOI: 10.1016/j.jmva.2024.105396
Jakub Woźny , Piotr Jaworski , Damian Jelito , Marcin Pitera , Agnieszka Wyłomańska
{"title":"Gaussian dependence structure pairwise goodness-of-fit testing based on conditional covariance and the 20/60/20 rule","authors":"Jakub Woźny ,&nbsp;Piotr Jaworski ,&nbsp;Damian Jelito ,&nbsp;Marcin Pitera ,&nbsp;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}
引用次数: 0
New multivariate Gini’s indices 新的多元基尼系数
IF 1.4 3区 数学
Journal of Multivariate Analysis Pub Date : 2024-11-28 DOI: 10.1016/j.jmva.2024.105394
Marco Capaldo , Jorge Navarro
{"title":"New multivariate Gini’s indices","authors":"Marco Capaldo ,&nbsp;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}
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
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
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