Journal of Multivariate Analysis最新文献

{"title":"A single risk approach to the semiparametric competing risks model with parametric Archimedean risk dependence","authors":"Simon M.S. Lo ,&nbsp;Ralf A. Wilke","doi":"10.1016/j.jmva.2023.105276","DOIUrl":"10.1016/j.jmva.2023.105276","url":null,"abstract":"<div><p>This paper considers a dependent competing risks model with the distribution of one risk being a semiparametric proportional hazards model, whereas the model for the other risks and the degree of risk dependence of an Archimedean copula are unknown. Identifiability is shown when there is at least one covariate with at least two values. Estimation is done by means of a <span><math><msqrt><mrow><mi>n</mi></mrow></msqrt></math></span>-consistent semiparametric two-step procedure. Applicability and attractive finite sample performance are demonstrated with the help of simulations. An application to unemployment duration confirms the importance of estimating rather than assuming risk dependence.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"201 ","pages":"Article 105276"},"PeriodicalIF":1.6,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0047259X23001227/pdfft?md5=ddb27eca7b668c675ebd4fe43bdd4f7b&pid=1-s2.0-S0047259X23001227-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138503930","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}

{"title":"Tests of independence and randomness for arbitrary data using copula-based covariances","authors":"Bouchra R. Nasri ,&nbsp;Bruno N. Rémillard","doi":"10.1016/j.jmva.2023.105273","DOIUrl":"10.1016/j.jmva.2023.105273","url":null,"abstract":"<div><p>In this article, we study tests of independence for data with arbitrary distributions in the non-serial case, i.e., for independent and identically distributed random vectors, as well as in the serial case, i.e., for time series. These tests are derived from copula-based covariances and their multivariate extensions using Möbius transforms. We find the asymptotic distributions<span> of these statistics under the null hypothesis of independence or randomness, as well as under contiguous alternatives. This enables us to find out locally most powerful test statistics for some alternatives, whatever the margins. Numerical experiments are performed for Wald’s type combinations of these statistics to assess the finite sample performance.</span></p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"201 ","pages":"Article 105273"},"PeriodicalIF":1.6,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138503932","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}

{"title":"On convergence and singularity of conditional copulas of multivariate Archimedean copulas, and conditional dependence","authors":"Thimo M. Kasper","doi":"10.1016/j.jmva.2023.105275","DOIUrl":"10.1016/j.jmva.2023.105275","url":null,"abstract":"<div><p>The present paper derives an explicit expression for (a version of) every uni- and multivariate conditional distribution (i.e., Markov kernel) of Archimedean copulas and uses this representation to generalize a recently established result, saying that in the class of multivariate Archimedean copulas standard uniform convergence implies weak convergence of almost all univariate Markov kernels, to arbitrary multivariate Markov kernels. Moreover, it is proved that an Archimedean copula is singular if, and only if, almost all uni- and multivariate Markov kernels are singular. These results are then applied to conditional Archimedean copulas which are reintroduced largely from a Markov kernel perspective and it is shown that convergence, singularity and conditional increasingness carry over from Archimedean copulas to their conditional copulas. As a consequence, the surprising fact is established that estimating (the generator of) an Archimedean copula directly yields an estimator of (the generator of) its conditional copula. Building upon that, we sketch the use and estimation of a conditional version of a recently introduced dependence measure as alternative to well-known conditional versions of association measures in order to study the dependence behavior of Archimedean models when fixing covariate values.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"201 ","pages":"Article 105275"},"PeriodicalIF":1.6,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0047259X23001215/pdfft?md5=76d6a3fa061bd2ac09cfb7d24782caaa&pid=1-s2.0-S0047259X23001215-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138503935","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}

{"title":"Copula-based conditional tail indices","authors":"Vincenzo Coia ,&nbsp;Harry Joe ,&nbsp;Natalia Nolde","doi":"10.1016/j.jmva.2023.105268","DOIUrl":"10.1016/j.jmva.2023.105268","url":null,"abstract":"<div><p><span>Consider a multivariate distribution of </span><span><math><mrow><mo>(</mo><mi>X</mi><mo>,</mo><mi>Y</mi><mo>)</mo></mrow></math></span>, where <span><math><mi>X</mi></math></span><span> is a vector of predictor variables and </span><span><math><mi>Y</mi></math></span><span> is a response variable. Results are obtained for comparing the conditional and marginal tail indices, </span><span><math><mrow><msub><mrow><mi>ξ</mi></mrow><mrow><mi>Y</mi><mo>|</mo><mi>X</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> and <span><math><msub><mrow><mi>ξ</mi></mrow><mrow><mi>Y</mi></mrow></msub></math></span>, based on conditional distributions <span><math><mrow><mo>{</mo><msub><mrow><mi>F</mi></mrow><mrow><mi>Y</mi><mo>|</mo><mi>X</mi></mrow></msub><mrow><mo>(</mo><mi>⋅</mi><mo>|</mo><mi>x</mi><mo>)</mo></mrow><mo>}</mo></mrow></math></span> and marginal distribution <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>Y</mi></mrow></msub></math></span><span>, respectively. For a multivariate distribution based on a copula, the conditional tail index can be decomposed into a product of copula-based conditional tail indices and the marginal tail index. In some applications, one may want </span><span><math><mrow><msub><mrow><mi>ξ</mi></mrow><mrow><mi>Y</mi><mo>|</mo><mi>X</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> to be non-constant, and some new copula families are derived to facilitate this.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"201 ","pages":"Article 105268"},"PeriodicalIF":1.6,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138503933","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}

{"title":"A novel positive dependence property and its impact on a popular class of concordance measures","authors":"Sebastian Fuchs,&nbsp;Marco Tschimpke","doi":"10.1016/j.jmva.2023.105259","DOIUrl":"https://doi.org/10.1016/j.jmva.2023.105259","url":null,"abstract":"<div><p>A novel positive dependence property is introduced, called positive measure inducing (PMI for short), being fulfilled by numerous copula classes, including Gaussian, Student <span><math><mi>t</mi></math></span>, Fréchet, Farlie–Gumbel–Morgenstern and Frank copulas; it is conjectured that even all positive quadrant dependent Archimedean copulas meet this property. From a geometric viewpoint, a PMI copula concentrates more mass near the main diagonal than in the opposite diagonal. A striking feature of PMI copulas is that they impose an ordering on a certain class of copula-induced measures of concordance, the latter originating in Edwards et al. (2004) and including Spearman’s rho <span><math><mi>ρ</mi></math></span> and Gini’s gamma <span><math><mi>γ</mi></math></span>, leading to numerous new inequalities such as <span><math><mrow><mn>3</mn><mi>γ</mi><mo>≥</mo><mn>2</mn><mi>ρ</mi></mrow></math></span>. The measures of concordance within this class are estimated using (classical) empirical copulas and the intrinsic construction via empirical checkerboard copulas, and the estimators’ asymptotic behavior is determined. Building upon the presented inequalities, asymptotic tests are constructed having the potential of being used for detecting whether the underlying dependence structure of a given sample is PMI, which in turn can be used for excluding certain copula families from model building. The excellent performance of the tests is demonstrated in a simulation study and by means of a real-data example.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"200 ","pages":"Article 105259"},"PeriodicalIF":1.6,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0047259X23001057/pdfft?md5=f90554c17c7d483e5a17da19024d99eb&pid=1-s2.0-S0047259X23001057-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138439175","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}

{"title":"Matrix-valued isotropic covariance functions with local extrema","authors":"Alfredo Alegría ,&nbsp;Xavier Emery","doi":"10.1016/j.jmva.2023.105250","DOIUrl":"https://doi.org/10.1016/j.jmva.2023.105250","url":null,"abstract":"<div><p>Multivariate random fields are commonly used in spatial statistics<span><span> and natural science to model coregionalized variables. In this context, the matrix-valued covariance function<span> plays a central role in capturing their spatial continuity and interdependence. This study aims to contribute to the literature on covariance modeling by proposing new parametric families of isotropic matrix-valued functions exhibiting non-monotonic behaviors, namely hole effects and cross-dimples. The benefit of the proposed models is shown on a </span></span>bivariate data set consisting of concentrations of airborne particulate matter.</span></p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"200 ","pages":"Article 105250"},"PeriodicalIF":1.6,"publicationDate":"2023-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138396036","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}

{"title":"Asymptotic properties of hierarchical clustering in high-dimensional settings","authors":"Kento Egashira ,&nbsp;Kazuyoshi Yata ,&nbsp;Makoto Aoshima","doi":"10.1016/j.jmva.2023.105251","DOIUrl":"https://doi.org/10.1016/j.jmva.2023.105251","url":null,"abstract":"<div><p>In this study, three asymptotic behaviors of hierarchical clustering are defined and studied with strict conditions under several asymptotic settings, from large samples to high dimensionality, when having two independent populations. We proceed with the current comprehension of the asymptotic properties of hierarchical clustering in high-dimensional, low-sample-size (HDLSS) settings. For high-dimensional data, the asymptotic properties of hierarchical clustering are demonstrated under mild and practical settings, and we present simulation studies and hierarchical clustering performance discussions. Furthermore, hierarchical clustering was theoretically investigated when both the dimension and sample size approach infinity, and we generalized a latent number of populations considering hierarchical clustering in multiclass HDLSS settings.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"199 ","pages":"Article 105251"},"PeriodicalIF":1.6,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0047259X23000970/pdfft?md5=8ddd59ad8fdac0f31ad39835b3a16f61&pid=1-s2.0-S0047259X23000970-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134656717","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}

{"title":"Statistical performance of quantile tensor regression with convex regularization","authors":"Wenqi Lu ,&nbsp;Zhongyi Zhu ,&nbsp;Rui Li ,&nbsp;Heng Lian","doi":"10.1016/j.jmva.2023.105249","DOIUrl":"10.1016/j.jmva.2023.105249","url":null,"abstract":"<div><p><span><span>In this paper, we consider high-dimensional quantile<span> tensor regression using a general convex decomposable regularizer and analyze the statistical performances of the estimator. The rates are stated in terms of the intrinsic dimension of the estimation problem, which is, roughly speaking, the dimension of the smallest subspace that contains the true coefficient. Previously, convex regularized tensor regression has been studied with a least squares loss, Gaussian tensorial predictors and Gaussian errors, with rates that depend on the Gaussian width of a convex set. Our results extend the previous work to nonsmooth quantile loss. To deal with the non-Gaussian setting, we use the concept of </span></span>Rademacher<span><span> complexity with appropriate concentration inequalities instead of the Gaussian width. For the multi-linear nuclear norm penalty, our Orlicz norm bound for the operator norm of a random matrix may be of independent interest. We validate the theoretical guarantees in numerical experiments. We also demonstrate advantage of quantile regression over mean regression, and compare the performance of convex </span>regularization method and nonconvex </span></span>decomposition method in solving quantile tensor regression problem in simulation studies.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"200 ","pages":"Article 105249"},"PeriodicalIF":1.6,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135764061","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}

{"title":"Non-asymptotic robustness analysis of regression depth median","authors":"Yijun Zuo","doi":"10.1016/j.jmva.2023.105247","DOIUrl":"https://doi.org/10.1016/j.jmva.2023.105247","url":null,"abstract":"<div><p>The maximum depth estimator (aka depth median) (<span><math><msubsup><mrow><mi>β</mi></mrow><mrow><mi>R</mi><mi>D</mi></mrow><mrow><mo>∗</mo></mrow></msubsup></math></span>) induced from regression depth (RD) of Rousseeuw and Hubert (1999) is one of the most prevailing estimators in regression. It possesses outstanding robustness similar to the univariate location counterpart. Indeed, <span><math><msubsup><mrow><mi>β</mi></mrow><mrow><mi>R</mi><mi>D</mi></mrow><mrow><mo>∗</mo></mrow></msubsup></math></span> can, asymptotically, resist up to 33% contamination without breakdown, in contrast to the 0% for the traditional (least squares and least absolute deviations) estimators (see Van Aelst and Rousseeuw (2000)). The results from Van Aelst and Rousseeuw (2000) are pioneering, yet they are limited to regression-symmetric populations (with a strictly positive density), the <span><math><mi>ϵ</mi></math></span>-contamination, maximum-bias model, and in asymptotical sense. With a fixed finite-sample size practice, the most prevailing measure of robustness for estimators is the finite-sample breakdown point (FSBP) (Donoho and Huber, 1983). Despite many attempts made in the literature, only sporadic partial results on FSBP for <span><math><msubsup><mrow><mi>β</mi></mrow><mrow><mi>R</mi><mi>D</mi></mrow><mrow><mo>∗</mo></mrow></msubsup></math></span> were obtained whereas an exact FSBP for <span><math><msubsup><mrow><mi>β</mi></mrow><mrow><mi>R</mi><mi>D</mi></mrow><mrow><mo>∗</mo></mrow></msubsup></math></span> remained open in the last twenty-plus years. Furthermore, is the asymptotic breakdown value <span><math><mrow><mn>1</mn><mo>/</mo><mn>3</mn></mrow></math></span> (the limit of an increasing sequence of finite-sample breakdown values) relevant in the finite-sample practice? (Or what is the difference between the finite-sample and the limit breakdown values?). Such discussions are yet to be given in the literature. This article addresses the above issues, revealing an intrinsic connection between the regression depth of <span><math><msubsup><mrow><mi>β</mi></mrow><mrow><mi>R</mi><mi>D</mi></mrow><mrow><mo>∗</mo></mrow></msubsup></math></span> and the newly obtained exact FSBP. It justifies the employment of <span><math><msubsup><mrow><mi>β</mi></mrow><mrow><mi>R</mi><mi>D</mi></mrow><mrow><mo>∗</mo></mrow></msubsup></math></span> as a robust alternative to the traditional estimators and demonstrates the necessity and the merit of using the FSBP in finite-sample real practice.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"199 ","pages":"Article 105247"},"PeriodicalIF":1.6,"publicationDate":"2023-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0047259X23000933/pdfft?md5=41b0163d4b47acc16c5399dda63160ea&pid=1-s2.0-S0047259X23000933-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91987809","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}

{"title":"On moments of truncated multivariate normal/independent distributions","authors":"Tsung-I Lin ,&nbsp;Wan-Lun Wang","doi":"10.1016/j.jmva.2023.105248","DOIUrl":"https://doi.org/10.1016/j.jmva.2023.105248","url":null,"abstract":"<div><p>Multivariate normal/independent (MNI) distributions contain many renowned heavy-tailed distributions such as the multivariate <span><math><mi>t</mi></math></span>, multivariate slash, multivariate contaminated normal, multivariate variance-gamma, and multivariate double exponential distributions. A frequent problem encountered in statistical analysis is the occurrence of truncated observations and non-normality such that theoretical moments are required for the estimation of the truncated multivariate normal/independent (TMNI) distributions. This paper is dedicated to deriving explicit expressions for the moments of the TMNI distributions with supports confined within a hyper-rectangle. A Monte Carlo experiment is undertaken to validate to the correctness of the proposed formulae for five selected members of the TMNI distributions. <span>R</span> scripts and data to reproduce the results are available in the GitHub repository.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"199 ","pages":"Article 105248"},"PeriodicalIF":1.6,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0047259X23000945/pdfft?md5=3cb17094e738a982bd8a526ea82d616f&pid=1-s2.0-S0047259X23000945-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91987808","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}