{"title":"Robust two-layer partition clustering of sparse multivariate functional data","authors":"Zhuo Qu, Wenlin Dai, Marc G. Genton","doi":"10.1016/j.ecosta.2023.03.002","DOIUrl":"10.1016/j.ecosta.2023.03.002","url":null,"abstract":"<div><div><span>A novel elastic time distance for sparse multivariate functional data is proposed and used to develop a robust distance-based two-layer partition clustering method. With this proposed distance, the new approach not only can detect correct clusters for sparse multivariate functional data under outlier settings but also can detect those outliers that do not belong to any clusters. Classical distance-based clustering methods such as density-based spatial clustering of applications with noise (DBSCAN), agglomerative hierarchical clustering, and </span><span><math><mi>K</mi></math></span>-medoids are extended to the sparse multivariate functional case based on the newly-proposed distance. Numerical experiments on simulated data highlight that the performance of the proposed algorithm is superior to the performances of existing model-based and extended distance-based methods. The effectiveness of the proposed approach is demonstrated using Northwest Pacific cyclone tracks data as an example.</div></div>","PeriodicalId":54125,"journal":{"name":"Econometrics and Statistics","volume":"40 ","pages":"Pages 153-172"},"PeriodicalIF":3.0,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75967413","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Review of Outlier Detection and Robust Estimation Methods for High Dimensional Time Series Data","authors":"Daniel Peña, Víctor J. Yohai","doi":"10.1016/j.ecosta.2023.02.001","DOIUrl":"10.1016/j.ecosta.2023.02.001","url":null,"abstract":"<div><div>Diagnostic procedures for finding outliers in high dimensional multivariate time series and robust estimation methods for these data are reviewed. First, methods for searching for outliers assuming that the data have been generated by a Dynamic Factor Model are presented. Then, other existing methods for detecting different types of multivariate time series outliers are analyzed. They include identifying outlying series and, also, looking for segments, or periods of time, where the series have unusual dynamics. Second, robust estimation methods are considered. Dynamic Principal Components, as a very general procedure to estimate the dynamic in a high dimensional data set, is introduced and different types of robust estimation of these components are reviewed. Dynamic Principal Components can be applied for robust estimation of Generalized Dynamic Factor models and some results are given. Finally, other methods proposed for robust estimation of high dimensional VAR models and other multivariate time series problems are also briefly discussed.</div></div>","PeriodicalId":54125,"journal":{"name":"Econometrics and Statistics","volume":"40 ","pages":"Pages 70-88"},"PeriodicalIF":3.0,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73265197","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the distribution-freeness of a test of angular symmetry based on halfspace depth","authors":"Alexander Dürre, Davy Paindaveine","doi":"10.1016/j.ecosta.2023.06.003","DOIUrl":"10.1016/j.ecosta.2023.06.003","url":null,"abstract":"<div><div>The problem of testing the null hypothesis of angular symmetry about a specified location in <span><math><msup><mi>R</mi><mi>d</mi></msup></math></span> is considered, with the focus being on a well-known test based on halfspace depth. In the bivariate case <span><math><mrow><mi>d</mi><mo>=</mo><mn>2</mn></mrow></math></span>, the exact null distribution of the corresponding test statistic is explicitly known and turns out not to depend on the underlying angularly symmetric distribution, so that the test is <em>distribution-free</em> under the null hypothesis. Distribution-freeness, which is of course crucial to make this test applicable in practice, is further investigated here. In dimension <span><math><mrow><mi>d</mi><mo>=</mo><mn>2</mn></mrow></math></span>, the reason why distribution-freeness holds is explained and it is shown through Monte Carlo exercises that distribution-freeness does not hold in dimension <span><math><mrow><mi>d</mi><mo>=</mo><mn>3</mn></mrow></math></span><span>. Through suitable concepts of hyperplane arrangements, it is then investigated why the test behaves differently for </span><span><math><mrow><mi>d</mi><mo>=</mo><mn>2</mn></mrow></math></span> and <span><math><mrow><mi>d</mi><mo>≥</mo><mn>3</mn></mrow></math></span><span>. The results reveal why distribution-freeness fails, and, for a particular sample size considered to ease the presentation, they show that deviations with respect to distribution-freeness, still for </span><span><math><mrow><mi>d</mi><mo>=</mo><mn>3</mn></mrow></math></span>, will actually remain very small. That these deviations will remain very small for other sample sizes is supported by a broader Monte Carlo exercise. Finally, a feasible conditional version of the test is proposed and asymptotic distribution-freeness is briefly discussed.</div></div>","PeriodicalId":54125,"journal":{"name":"Econometrics and Statistics","volume":"40 ","pages":"Pages 39-53"},"PeriodicalIF":3.0,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73684408","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Lorenzo Camponovo, Olivier Scaillet, Fabio Trojani
{"title":"Predictability hidden by Anomalous Observations in Financial Data","authors":"Lorenzo Camponovo, Olivier Scaillet, Fabio Trojani","doi":"10.1016/j.ecosta.2024.03.004","DOIUrl":"10.1016/j.ecosta.2024.03.004","url":null,"abstract":"<div><div>Testing procedures for predictive regressions involving lagged autoregressive variables produce a suboptimal inference in presence of minor violations of ideal assumptions. A novel testing framework based on resampling methods that exhibits resistance to such violations and is reliable also in models with nearly integrated regressors is introduced. To achieve this objective, the robustness of resampling procedures for time series are defined by deriving new formulas quantifying their quantile breakdown point. For both the block bootstrap and subsampling, these formulas show a very low quantile breakdown point. To overcome this problem, a robust and fast resampling scheme applicable to a broad class of time series settings is proposed. This framework is also suitable for multi-predictor settings, particularly when the data only approximately conform to a predictive regression model. Monte Carlo simulations provide substantial evidence for the significant improvements offered by this robust approach. Using the proposed resampling methods, empirical coverages and rejection frequencies are very close to the nominal levels, both in the presence and absence of small deviations from the ideal model assumptions. Empirical analysis reveals robust evidence of market return predictability, previously obscured by anomalous observations, both in- and out-of-sample.</div></div>","PeriodicalId":54125,"journal":{"name":"Econometrics and Statistics","volume":"40 ","pages":"Pages 103-125"},"PeriodicalIF":3.0,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140583124","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Zhi Yang Tho, Ding Ding, Francis K.C. Hui, A.H. Welsh, Tao Zou
{"title":"On the Robust Estimation of Spatial Autoregressive Models","authors":"Zhi Yang Tho, Ding Ding, Francis K.C. Hui, A.H. Welsh, Tao Zou","doi":"10.1016/j.ecosta.2023.01.004","DOIUrl":"10.1016/j.ecosta.2023.01.004","url":null,"abstract":"<div><div><span><span>The spatial autoregressive (SAR) model is commonly used for cross-sectional data with spatial dependence in the response variable. A robust M-estimator for the SAR model with independent normal </span>random errors<span> is proposed, which is resistant to extreme contamination or outliers in the data. The proposed estimator is defined by a set of robust estimating functions derived by modifying the estimating functions for the standard maximum likelihood (ML) estimator using the Huber function. An iterative algorithm based on iteratively reweighted least squares and a </span></span>fixed point<span><span> method is provided to compute the robust M-estimator. The proposed estimator is shown to be Fisher-consistent under the core model, has a bounded influence function, and is asymptotically normally distributed. A closed-form expression for the asymptotic covariance matrix estimator under the core model is derived, and used to study the asymptotic relative efficiency of the proposed estimator. Simulation studies demonstrate that the proposed robust M-estimator greatly outperforms the ML estimator as well as several other non-robust estimators of the SAR model, in terms of both estimation and inference under different contamination scenarios. Additionally, the proposed estimator offers comparable performance to some </span>robust estimators of the SAR model under contamination. Applying the robust M-estimator for the SAR model to the U.S. federal grants and U.S. Nielsen Local Television View datasets reveals strong positive spatial dependence in the grant value among counties, insignificant positive effect of news watching on grant distribution, and evidence of outliers in the data. This results in different conclusions from those obtained using the ML estimator.</span></div></div>","PeriodicalId":54125,"journal":{"name":"Econometrics and Statistics","volume":"40 ","pages":"Pages 89-102"},"PeriodicalIF":3.0,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87821883","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On approximate robust confidence distributions","authors":"Elena Bortolato, Laura Ventura","doi":"10.1016/j.ecosta.2023.04.006","DOIUrl":"10.1016/j.ecosta.2023.04.006","url":null,"abstract":"<div><div>A confidence distribution is a complete tool for making frequentist inference for a parameter of interest based on an assumed parametric model. Indeed, it provides point estimates, along with confidence intervals, allows to define rejection regions for testing unilateral and bilateral hypotheses, to assign measures of evidence or levels of confidence to prespecified regions of the parameter space, and to compare the parameter of interest with other parameters from other studies. The aim is to discuss robust confidence distributions derived from unbiased <span><math><mi>M</mi></math></span>-estimating functions, which provide bounded-influence inference for a parameter of interest, when the assumed central model is just an approximate parametric model or in the presence of deviant values in the observed data. Paralleling likelihood-based results and extending results available for robust scoring rules, two methods are proposed for deriving robust confidence distributions: the first one uses the asymptotic theory of robust pivotal quantities and the second one is based on simulation methods. An application and a simulation study are illustrated in the context of non-inferiority and superiority testing.</div></div>","PeriodicalId":54125,"journal":{"name":"Econometrics and Statistics","volume":"40 ","pages":"Pages 54-69"},"PeriodicalIF":3.0,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74925471","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the consistency of K-sign depth tests","authors":"Kevin Leckey, Mirko Jakubzik, Christine H. Müller","doi":"10.1016/j.ecosta.2023.10.002","DOIUrl":"10.1016/j.ecosta.2023.10.002","url":null,"abstract":"<div><div>The consistency of the so-called <span><math><mi>K</mi></math></span>-sign depth tests is considered. These tests are based on the <span><math><mi>K</mi></math></span>-sign depth, which originated from the simplicial regression depth, but is easier to compute. The <span><math><mi>K</mi></math></span>-sign depth tests use only the signs of residuals and are equivalent to the classical sign test for <span><math><mrow><mi>K</mi><mo>=</mo><mn>2</mn></mrow></math></span>. However, <span><math><mi>K</mi></math></span>-sign depth tests with <span><math><mrow><mi>K</mi><mo>≥</mo><mn>3</mn></mrow></math></span> show a much better power than the classical sign tests in simulation studies. This property is attributed to the consistency of these tests for <span><math><mrow><mi>K</mi><mo>=</mo><mn>3</mn></mrow></math></span>. After deriving a general condition for consistency, it is shown that this condition is in particular satisfied for several relevant hypotheses in polynomial regression models.</div></div>","PeriodicalId":54125,"journal":{"name":"Econometrics and Statistics","volume":"40 ","pages":"Pages 24-38"},"PeriodicalIF":3.0,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135762405","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Robust Clustering with Normal Mixture Models: A Pseudo β-Likelihood Approach","authors":"Soumya Chakraborty, Ayanendranath Basu, Abhik Ghosh","doi":"10.1016/j.ecosta.2023.10.004","DOIUrl":"10.1016/j.ecosta.2023.10.004","url":null,"abstract":"<div><div><span><span>As in other estimation scenarios, likelihood based estimation in the normal mixture set-up is highly non-robust against model misspecification and presence of outliers (apart from being an ill-posed optimization problem). A robust alternative to the ordinary likelihood approach for this estimation problem is proposed which performs simultaneous estimation and data clustering and leads to subsequent </span>anomaly detection. To invoke robustness, the methodology based on the minimization of the density power divergence (or alternatively, the maximization of the </span><span><math><mi>β</mi></math></span><span>-likelihood) is utilized under suitable constraints. An iteratively reweighted least squares<span><span> approach has been followed in order to compute the proposed estimators for the component means (or equivalently cluster centers) and component dispersion matrices which leads to simultaneous data clustering. Some exploratory techniques are also suggested for anomaly detection, a problem of great importance in the domain of statistics and machine learning. The proposed method is validated with simulation studies under different set-ups; it performs competitively or better compared to the popular existing methods like K-medoids, TCLUST, trimmed K-means and MCLUST, especially when the mixture components (i.e., the clusters) share regions with significant overlap or outlying clusters exist with small but non-negligible weights (particularly in higher dimensions). Two real datasets are also used to illustrate the performance of the newly proposed method in comparison with others along with an application in </span>image processing<span>. The proposed method detects the clusters with lower misclassification rates and successfully points out the outlying (anomalous) observations from these datasets.</span></span></span></div></div>","PeriodicalId":54125,"journal":{"name":"Econometrics and Statistics","volume":"40 ","pages":"Pages 173-194"},"PeriodicalIF":3.0,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135410228","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Andreas Alfons, Aurore Archimbaud, Klaus Nordhausen, Anne Ruiz-Gazen
{"title":"Tandem clustering with invariant coordinate selection","authors":"Andreas Alfons, Aurore Archimbaud, Klaus Nordhausen, Anne Ruiz-Gazen","doi":"10.1016/j.ecosta.2024.03.002","DOIUrl":"10.1016/j.ecosta.2024.03.002","url":null,"abstract":"<div><div>For multivariate data, tandem clustering is a well-known technique aiming to improve cluster identification through initial dimension reduction. Nevertheless, the usual approach using principal component analysis (PCA) has been criticized for focusing solely on inertia so that the first components do not necessarily retain the structure of interest for clustering. To address this limitation, a new tandem clustering approach based on invariant coordinate selection (ICS) is proposed. By jointly diagonalizing two scatter matrices, ICS is designed to find structure in the data while providing affine invariant components. Certain theoretical results have been previously derived and guarantee that under some elliptical mixture models, the group structure can be highlighted on a subset of the first and/or last components. However, ICS has garnered minimal attention within the context of clustering. Two challenges associated with ICS include choosing the pair of scatter matrices and selecting the components to retain. For effective clustering purposes, it is demonstrated that the best scatter pairs consist of one scatter matrix capturing the within-cluster structure and another capturing the global structure. For the former, local shape or pairwise scatters are of great interest, as is the minimum covariance determinant (MCD) estimator based on a carefully chosen subset size that is smaller than usual. The performance of ICS as a dimension reduction method is evaluated in terms of preserving the cluster structure in the data. In an extensive simulation study and empirical applications with benchmark data sets, various combinations of scatter matrices as well as component selection criteria are compared in situations with and without outliers. Overall, the new approach of tandem clustering with ICS shows promising results and clearly outperforms the PCA-based approach.</div></div>","PeriodicalId":54125,"journal":{"name":"Econometrics and Statistics","volume":"40 ","pages":"Pages 126-152"},"PeriodicalIF":3.0,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140198960","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Center-outward Rank- and Sign-based VARMA Portmanteau Tests: Chitturi, Hosking, and Li–McLeod revisited","authors":"Marc Hallin, Hang Liu","doi":"10.1016/j.ecosta.2023.01.006","DOIUrl":"10.1016/j.ecosta.2023.01.006","url":null,"abstract":"<div><div><span>The pseudo-Gaussian portmanteau tests of Chitturi, Hosking, and Li and McLeod for VARMA models are revisited from a Le Cam perspective, providing a precise and more rigorous description of the asymptotic behavior of the multivariate portmanteau test statistic, which depends on the dimension </span><span><math><mi>d</mi></math></span> of the observations, the number <span><math><mi>m</mi></math></span> of lags involved, and the length <span><math><mi>n</mi></math></span> of the observation period. Then, based on the concepts of center-outward ranks and signs recently developed (Hallin, del Barrio, Cuesta-Albertos, and Matrán, <em>Annals of Statistics</em><span> 49, 1139–1165, 2021), a class of multivariate rank- and sign-based portmanteau test statistics is proposed which, under the null hypothesis and under a broad family of innovation densities, can be approximated by an asymptotically chi-square variable. The asymptotic properties of these tests are derived; simulations demonstrate their advantages over their classical pseudo-Gaussian counterpart.</span></div></div>","PeriodicalId":54125,"journal":{"name":"Econometrics and Statistics","volume":"40 ","pages":"Pages 1-23"},"PeriodicalIF":3.0,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89047470","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}