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Efficient calibration of computer models with multivariate output 高效校准多变量输出的计算机模型
IF 1.6 3区 数学
Journal of Multivariate Analysis Pub Date : 2024-03-21 DOI: 10.1016/j.jmva.2024.105315
Yang Sun, Xiangzhong Fang
{"title":"Efficient calibration of computer models with multivariate output","authors":"Yang Sun,&nbsp;Xiangzhong Fang","doi":"10.1016/j.jmva.2024.105315","DOIUrl":"10.1016/j.jmva.2024.105315","url":null,"abstract":"<div><p>The classical calibration procedures of computer models only concern the univariate output, which would not be satisfied in practice. Multivariate output is gradually more prevalent in a wide range of real-world applications, which motivates us to develop a new calibration procedure to extend the classical calibration methods to multivariate cases. In this work, we propose an efficient calibration procedure for multivariate output within restricted correlation. First, we construct an estimator of the discrepancy function between the true process and the computer model by the local linear approximation, then obtain an estimator of the calibration parameter by the weighted profile least squares and establish its asymptotic properties. In addition, we also develop an estimator of the calibration parameter in a special situation, whose asymptotic normality has been derived. Numerical studies including simulations and an application to composite fuselage simulation verify the efficiency of the proposed calibration procedure.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"202 ","pages":"Article 105315"},"PeriodicalIF":1.6,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140280995","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 extreme quantile region estimation under heavy-tailed elliptical distributions 重尾椭圆分布下的极值量级区域估计
IF 1.6 3区 数学
Journal of Multivariate Analysis Pub Date : 2024-03-20 DOI: 10.1016/j.jmva.2024.105314
Jaakko Pere , Pauliina Ilmonen , Lauri Viitasaari
{"title":"On extreme quantile region estimation under heavy-tailed elliptical distributions","authors":"Jaakko Pere ,&nbsp;Pauliina Ilmonen ,&nbsp;Lauri Viitasaari","doi":"10.1016/j.jmva.2024.105314","DOIUrl":"10.1016/j.jmva.2024.105314","url":null,"abstract":"<div><p>Consider the estimation of an extreme quantile region corresponding to a very small probability. Estimation of extreme quantile regions is important but difficult since extreme regions contain only a few or no observations. In this article, we propose an affine equivariant extreme quantile region estimator for heavy-tailed elliptical distributions. The estimator is constructed by extending a well-known univariate extreme quantile estimator. Consistency of the estimator is proved under estimated location and scatter. The practicality of the developed estimator is illustrated with simulations and a real data example.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"202 ","pages":"Article 105314"},"PeriodicalIF":1.6,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0047259X24000216/pdfft?md5=9428a79c05ecd5a039851cfc8de51bac&pid=1-s2.0-S0047259X24000216-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140282482","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
Online stochastic Newton methods for estimating the geometric median and applications 估计几何中值的在线随机牛顿方法及其应用
IF 1.6 3区 数学
Journal of Multivariate Analysis Pub Date : 2024-03-19 DOI: 10.1016/j.jmva.2024.105313
Antoine Godichon-Baggioni , Wei Lu
{"title":"Online stochastic Newton methods for estimating the geometric median and applications","authors":"Antoine Godichon-Baggioni ,&nbsp;Wei Lu","doi":"10.1016/j.jmva.2024.105313","DOIUrl":"https://doi.org/10.1016/j.jmva.2024.105313","url":null,"abstract":"<div><p>In the context of large samples, a small number of individuals might spoil basic statistical indicators like the mean. It is difficult to detect automatically these atypical individuals, and an alternative strategy is using robust approaches. This paper focuses on estimating the geometric median of a random variable, which is a robust indicator of central tendency. In order to deal with large samples of data arriving sequentially, online stochastic Newton algorithms for estimating the geometric median are introduced and we give their rates of convergence. Since estimates of the median and those of the Hessian matrix can be recursively updated, we also determine confidences intervals of the median in any designated direction and perform online statistical tests.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"202 ","pages":"Article 105313"},"PeriodicalIF":1.6,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140191763","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 consistent test of equality of distributions for Hilbert-valued random elements 希尔伯特值随机元素分布相等的一致性检验
IF 1.6 3区 数学
Journal of Multivariate Analysis Pub Date : 2024-03-15 DOI: 10.1016/j.jmva.2024.105312
Gil González–Rodríguez , Ana Colubi , Wenceslao González–Manteiga , Manuel Febrero–Bande
{"title":"A consistent test of equality of distributions for Hilbert-valued random elements","authors":"Gil González–Rodríguez ,&nbsp;Ana Colubi ,&nbsp;Wenceslao González–Manteiga ,&nbsp;Manuel Febrero–Bande","doi":"10.1016/j.jmva.2024.105312","DOIUrl":"10.1016/j.jmva.2024.105312","url":null,"abstract":"<div><p>Two independent random elements taking values in a separable Hilbert space are considered. The aim is to develop a test with bootstrap calibration to check whether they have the same distribution or not. A transformation of both random elements into a new separable Hilbert space is considered so that the equality of expectations of the transformed random elements is equivalent to the equality of distributions. Thus, a bootstrap test procedure to check the equality of means can be used in order to solve the original problem. It will be shown that both the asymptotic and bootstrap approaches proposed are asymptotically correct and consistent. The results can be applied, for example, in functional data analysis. In practice, the test can be solved with simple operations in the original space without applying the mentioned transformation, which is used only to guarantee the theoretical results. Empirical results and comparisons with related methods support and complement the theory.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"202 ","pages":"Article 105312"},"PeriodicalIF":1.6,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0047259X24000198/pdfft?md5=6bc123f9555c6b95bcd432fc26329ddb&pid=1-s2.0-S0047259X24000198-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140152986","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
Change point analysis of functional variance function with stationary error 具有静态误差的函数方差函数的变化点分析
IF 1.6 3区 数学
Journal of Multivariate Analysis Pub Date : 2024-03-11 DOI: 10.1016/j.jmva.2024.105311
Qirui Hu
{"title":"Change point analysis of functional variance function with stationary error","authors":"Qirui Hu","doi":"10.1016/j.jmva.2024.105311","DOIUrl":"10.1016/j.jmva.2024.105311","url":null,"abstract":"<div><p>An asymptotically correct test for an abrupt break in functional variance function of measurement error in the functional sequence and the confidence interval of change point is constructed. Under general assumptions, the test and detection procedure conducted by Spline-backfitted kernel smoothing, i.e., recovering trajectories with B-spline and estimating variance function with kernel regression, enjoy oracle efficiency, namely, the proposed procedure is asymptotically indistinguishable from that with accurate trajectories. Furthermore, a consistent algorithm for multiple change points based on the binary segment is derived. Extensive simulation studies reveal a positive confirmation of the asymptotic theory. The proposed method is applied to analyze EEG data.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"202 ","pages":"Article 105311"},"PeriodicalIF":1.6,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140152987","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 heavy-tailed risks under Gaussian copula: The effects of marginal transformation 高斯共轭下的重尾风险：边际转换的影响
IF 1.6 3区 数学
Journal of Multivariate Analysis Pub Date : 2024-03-01 DOI: 10.1016/j.jmva.2024.105310
Bikramjit Das , Vicky Fasen-Hartmann
{"title":"On heavy-tailed risks under Gaussian copula: The effects of marginal transformation","authors":"Bikramjit Das ,&nbsp;Vicky Fasen-Hartmann","doi":"10.1016/j.jmva.2024.105310","DOIUrl":"https://doi.org/10.1016/j.jmva.2024.105310","url":null,"abstract":"<div><p>In this paper, we compute multivariate tail risk probabilities where the marginal risks are heavy-tailed and the dependence structure is a Gaussian copula. The marginal heavy-tailed risks are modeled using regular variation which leads to a few interesting consequences. First, as the threshold increases, we note that the rate of decay of probabilities of tail sets varies depending on the type of tail sets considered and the Gaussian correlation matrix. Second, we discover that although any multivariate model with a Gaussian copula admits the so-called asymptotic tail independence property, the joint tail behavior under heavier tailed marginal variables is structurally distinct from that under Gaussian marginal variables. The results obtained are illustrated using examples and simulations.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"202 ","pages":"Article 105310"},"PeriodicalIF":1.6,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140031062","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
High-dimensional nonconvex LASSO-type M-estimators 高维非凸 LASSO 型 M 估计器
IF 1.6 3区 数学
Journal of Multivariate Analysis Pub Date : 2024-02-27 DOI: 10.1016/j.jmva.2024.105303
Jad Beyhum , François Portier
{"title":"High-dimensional nonconvex LASSO-type M-estimators","authors":"Jad Beyhum ,&nbsp;François Portier","doi":"10.1016/j.jmva.2024.105303","DOIUrl":"https://doi.org/10.1016/j.jmva.2024.105303","url":null,"abstract":"<div><p>A theory is developed to examine the convergence properties of <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>-norm penalized high-dimensional <span><math><mi>M</mi></math></span>-estimators, with nonconvex risk and unrestricted domain. Under high-level conditions, the estimators are shown to attain the rate of convergence <span><math><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn>0</mn></mrow></msub><msqrt><mrow><mo>log</mo><mrow><mo>(</mo><mi>n</mi><mi>d</mi><mo>)</mo></mrow><mo>/</mo><mi>n</mi></mrow></msqrt></mrow></math></span>, where <span><math><msub><mrow><mi>s</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> is the number of nonzero coefficients of the parameter of interest. Sufficient conditions for our main assumptions are then developed and finally used in several examples including robust linear regression, binary classification and nonlinear least squares.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"202 ","pages":"Article 105303"},"PeriodicalIF":1.6,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139986808","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
Nonlinear sufficient dimension reduction for distribution-on-distribution regression 分布对分布回归的非线性充分降维
IF 1.6 3区 数学
Journal of Multivariate Analysis Pub Date : 2024-02-27 DOI: 10.1016/j.jmva.2024.105302
Qi Zhang, Bing Li, Lingzhou Xue
{"title":"Nonlinear sufficient dimension reduction for distribution-on-distribution regression","authors":"Qi Zhang,&nbsp;Bing Li,&nbsp;Lingzhou Xue","doi":"10.1016/j.jmva.2024.105302","DOIUrl":"https://doi.org/10.1016/j.jmva.2024.105302","url":null,"abstract":"<div><p>We introduce a new approach to nonlinear sufficient dimension reduction in cases where both the predictor and the response are distributional data, modeled as members of a metric space. Our key step is to build universal kernels (cc-universal) on the metric spaces, which results in reproducing kernel Hilbert spaces for the predictor and response that are rich enough to characterize the conditional independence that determines sufficient dimension reduction. For univariate distributions, we construct the universal kernel using the Wasserstein distance, while for multivariate distributions, we resort to the sliced Wasserstein distance. The sliced Wasserstein distance ensures that the metric space possesses similar topological properties to the Wasserstein space, while also offering significant computation benefits. Numerical results based on synthetic data show that our method outperforms possible competing methods. The method is also applied to several data sets, including fertility and mortality data and Calgary temperature data.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"202 ","pages":"Article 105302"},"PeriodicalIF":1.6,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139986807","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
Linearized maximum rank correlation estimation when covariates are functional 协变量为函数时的线性化最大秩相关估计
IF 1.6 3区 数学
Journal of Multivariate Analysis Pub Date : 2024-02-24 DOI: 10.1016/j.jmva.2024.105301
Wenchao Xu , Xinyu Zhang , Hua Liang
{"title":"Linearized maximum rank correlation estimation when covariates are functional","authors":"Wenchao Xu ,&nbsp;Xinyu Zhang ,&nbsp;Hua Liang","doi":"10.1016/j.jmva.2024.105301","DOIUrl":"https://doi.org/10.1016/j.jmva.2024.105301","url":null,"abstract":"<div><p>This paper extends the linearized maximum rank correlation (LMRC) estimation proposed by Shen et al. (2023) to the setting where the covariate is a function. However, this extension is nontrivial due to the difficulty of inverting the covariance operator, which may raise the ill-posed inverse problem, for which we integrate the functional principal component analysis to the LMRC procedure. The proposed estimator is robust to outliers in response and computationally efficient. We establish the rate of convergence of the proposed estimator, which is minimax optimal under certain smoothness assumptions. Furthermore, we extend the proposed estimation procedure to handle discretely observed functional covariates, including both sparse and dense sampling designs, and establish the corresponding rate of convergence. Simulation studies demonstrate that the proposed estimators outperform the other existing methods for some examples. Finally, we apply our method to a real data to illustrate its usefulness.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"202 ","pages":"Article 105301"},"PeriodicalIF":1.6,"publicationDate":"2024-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139975931","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
Variable selection in multivariate regression models with measurement error in covariates 具有协变量测量误差的多元回归模型中的变量选择
IF 1.6 3区 数学
Journal of Multivariate Analysis Pub Date : 2024-02-17 DOI: 10.1016/j.jmva.2024.105299
Jingyu Cui , Grace Y. Yi
{"title":"Variable selection in multivariate regression models with measurement error in covariates","authors":"Jingyu Cui ,&nbsp;Grace Y. Yi","doi":"10.1016/j.jmva.2024.105299","DOIUrl":"https://doi.org/10.1016/j.jmva.2024.105299","url":null,"abstract":"<div><p>Multivariate regression models have been broadly used in analyzing data having multi-dimensional response variables. The use of such models is, however, impeded by the presence of measurement error and spurious variables. While data with such features are common in applications, there has been little work available concerning these features jointly. In this article, we consider variable selection under multivariate regression models with covariates subject to measurement error. To gain flexibility, we allow the dimensions of the covariate and response variables to be either fixed or diverging as the sample size increases. A new regularized method is proposed to handle both variable selection and measurement error effects for error-contaminated data. Our proposed penalized bias-corrected least squares method offers flexibility in selecting the penalty function from a class of functions with different features. Importantly, our method does not require full distributional assumptions for the associated variables, thereby broadening its applicability. We rigorously establish theoretical results and describe a computationally efficient procedure for the proposed method. Numerical studies confirm the satisfactory performance of the proposed method under finite settings, and also demonstrate deleterious effects of ignoring measurement error in inferential procedures.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"202 ","pages":"Article 105299"},"PeriodicalIF":1.6,"publicationDate":"2024-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139998890","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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