International Statistical Review最新文献

{"title":"Discussion of ‘Robust distance covariance’ by S. Leyder, J. Raymaekers and P. J. Rousseeuw","authors":"Hallin Marc,&nbsp;Davide La Vecchia,&nbsp;Hang Liu,&nbsp;Xinyi Xu","doi":"10.1111/insr.70014","DOIUrl":"https://doi.org/10.1111/insr.70014","url":null,"abstract":"<p>The distance covariance in Székely et al. (<span>2007</span>) was introduced for \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mfenced>\u0000 <mrow>\u0000 <msup>\u0000 <mi>ℝ</mi>\u0000 <msub>\u0000 <mi>d</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 </msup>\u0000 <mo>×</mo>\u0000 <msup>\u0000 <mi>ℝ</mi>\u0000 <msub>\u0000 <mi>d</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 </msup>\u0000 </mrow>\u0000 </mfenced>\u0000 </mrow>\u0000 <annotation>$$ left({mathrm{mathbb{R}}}&amp;amp;#x0005E;{d_1}times {mathrm{mathbb{R}}}&amp;amp;#x0005E;{d_2}right) $$</annotation>\u0000 </semantics></math>-valued data. Building on the concepts introduced in Chernozhukov et al. (<span>2017</span>) and Hallin et al. (<span>2021</span>), the corresponding rank-based versions only came some 10 years later, with Shi et al. (<span>2022a</span>, <span>2022b</span>, <span>2024</span>) and, in a slightly different form, with Deb and Sen (<span>2023</span>). We only briefly sketch their definitions (Section 2.1) and suggest (Section 2.2) how to robustify them, along the same lines as in [LRR], into statistics with redescending influence functions.</p><p>Section 2 takes care of distance covariances for multivariate real data. Further extensions, however, are highly desirable and have not been explored so far. In this section, we are sketching a possible extension to directional data, that is, to random directions distributed on hyperspheres. We conjecture that extensions to other compact nonlinear Riemannian manifolds, such as tori and products of hyperspheres, are feasible using the same methodology, along with the nonparametric tools for Riemannian manifolds developed by Hallin and Liu (<span>2024</span>). Here, we restrict the exposition to the case of hyperspheres.</p><p>Building on the measure-transportation-based notions of directional ranks and signs defined in Hallin et al. (<span>2024</span>), we show how the ‘robustness via transformation’ principle emphasized by [LRR] extends beyond the case of bivariate independence and also applies in higher-dimensional Euclidean spaces and on compact manifolds. The case of directional variables (taking values on (hyper)spheres) is given special attention: although (hyper)spheres are not metric spaces of the strong negative type, we introduce a class of pertinent directional distance covariance test statistics and illustrate their applicability. We hope that this note will open the door to further research directions in line with [LRR].</p>","PeriodicalId":14479,"journal":{"name":"International Statistical Review","volume":"94 1","pages":"40-53"},"PeriodicalIF":1.8,"publicationDate":"2026-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/insr.70014","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147683591","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":"Fisher Meets Bayes: The Value of Randomisation for Bayesian Inference of Causal Effects","authors":"Thomas Leavitt","doi":"10.1111/insr.12598","DOIUrl":"https://doi.org/10.1111/insr.12598","url":null,"abstract":"<div>\u0000 \u0000 <p>For a Bayesian agent with beliefs about the relationship between covariates and potential outcomes, deterministically selecting an assignment that yields optimal covariate balance rationally dominates randomisation. However, randomisation—by enabling control over the probabilities of erroneous causal conclusions due to unknown covariate imbalances—offers insurance against the possibility that an agent's beliefs may be misleading. For the most part, such rational justifications for optimum assignment have presupposed the framework of Bayesian inference, while such epistemic justifications for randomisation have presupposed the framework of significance testing. In this paper, I build on a conception of balance that seems inextricable from the significance testing framework, Fisherian balance, to show that it implies an analogous epistemic justification for randomisation within the framework of Bayesian inference. Consequently, for the choice between optimum and random assignment, this paper shows that epistemic justifications need not be wedded to significance testing nor must Bayesian inference be wedded to rational justifications.</p>\u0000 </div>","PeriodicalId":14479,"journal":{"name":"International Statistical Review","volume":"94 1","pages":"188-201"},"PeriodicalIF":1.8,"publicationDate":"2026-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147683941","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 Frequency and Probability Weights: An In-Depth Look at Duelling Weights","authors":"Tuo Lin,&nbsp;Ruohui Chen,&nbsp;Jinyuan Liu,&nbsp;Tsungchin Wu,&nbsp;Toni T. Gui,&nbsp;Yangyi Li,&nbsp;Xinyi Huang,&nbsp;Kun Yang,&nbsp;Guanqing Chen,&nbsp;Tian Chen,&nbsp;David R. Strong,&nbsp;Karen Messer,&nbsp;Xin M. Tu","doi":"10.1111/insr.12594","DOIUrl":"10.1111/insr.12594","url":null,"abstract":"<div>\u0000 \u0000 <p>Probability weights have been widely used in addressing selection bias arising from a variety of contexts. Common examples of probability weights include sampling weights, missing data weights, and propensity score weights. Frequency weights, which are used to control for varying variabilities of aggregated outcomes, are both conceptually and analytically different from probability weights. Popular software such as R, SAS and STATA support both types of weights. Many users, including professional statisticians, become bewildered when they see identical estimates, but different standard errors and \u0000<span></span><math>\u0000 <mi>p</mi></math>-values when probability weights are treated as frequency weights. Some even completely ignore the difference between the two types of weights and treat them as the same. Although a large body of literature exists on each type of weights, we have found little, if any, discussion that provides head-to-head comparisons of the two types of weights and associated inference methods. In this paper, we unveil the conceptual and analytic differences between the two types of weights within the context of parametric and semi-parametric generalised linear models (GLM) and discuss valid inference for each type of weights. To the best of our knowledge, this is the first paper that looks into such differences by identifying the conditions under which the two types of weights can be treated the same analytically and providing clear guidance on the appropriate statistical models and inference procedures for each type of weights. We illustrate these considerations using real study data.</p>\u0000 </div>","PeriodicalId":14479,"journal":{"name":"International Statistical Review","volume":"94 1","pages":"121-139"},"PeriodicalIF":1.8,"publicationDate":"2026-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142182486","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":"Alternative Approaches for Estimating Highest-Density Regions","authors":"Nina Deliu,&nbsp;Brunero Liseo","doi":"10.1111/insr.12592","DOIUrl":"10.1111/insr.12592","url":null,"abstract":"<p>Among the variety of statistical intervals, highest-density regions (HDRs) stand out for their ability to effectively summarise a distribution or sample, unveiling its distinctive and salient features. An HDR represents the minimum size set that satisfies a certain probability coverage, and current methods for their computation require knowledge or estimation of the underlying probability distribution or density \u0000<span></span><math>\u0000 <mi>f</mi></math>. In this work, we illustrate a broader framework for computing HDRs, which generalises the classical density quantile method. The framework is based on <i>neighbourhood</i> measures, that is, measures that preserve the order induced in the sample by \u0000<span></span><math>\u0000 <mi>f</mi></math>, and include the density \u0000<span></span><math>\u0000 <mi>f</mi></math> as a special case. We explore a number of suitable distance-based measures, such as the \u0000<span></span><math>\u0000 <mi>k</mi></math>-nearest neighbourhood distance, and some probabilistic variants based on <i>copula models</i>. An extensive comparison is provided, showing the advantages of the copula-based strategy, especially in those scenarios that exhibit complex structures (e.g. multimodalities or particular dependencies). Finally, we discuss the practical implications of our findings for estimating HDRs in real-world applications.</p>","PeriodicalId":14479,"journal":{"name":"International Statistical Review","volume":"94 1","pages":"97-120"},"PeriodicalIF":1.8,"publicationDate":"2026-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/insr.12592","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142182503","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":"Adjusting Self-Protective and Non-Response Behaviours in Sensitive Prevalence Estimation by a Two-Stage Multilevel Randomised Response Technique","authors":"Martin T. Lukusa,&nbsp;Pier Francesco Perri,&nbsp;Shu-Hui Hsieh","doi":"10.1111/insr.12597","DOIUrl":"https://doi.org/10.1111/insr.12597","url":null,"abstract":"<div>\u0000 \u0000 <p>When using the customary direct questioning approach to collect sensitive information in a survey, some respondents may have no problem disclosing their true status or opinion, while others may be reluctant to reveal them. The problem of response bias is likely to arise as some responses tend to be more socially desirable than truthful. Hence, the indirect questioning approach can be used to guarantee privacy protection and reduce the influence of social desirability bias. This paper introduces a new technique which combines, both the direct and indirect questioning approaches and allows Bayesian estimates of the prevalence of multisensitive attributes to be obtained by taking into account the estimated proportion of honest respondents under direct questioning. Our proposal stems from a real survey in Taiwan and is illustrated with two motivating examples concerning voting behaviours and sexual identity. The empirical analysis reinforces that the proposed two-stage multilevel method is satisfactory in mitigating the effects of respondents' self-protective behaviour, and produces results that are more reliable than those based on the traditional direct questioning approach and better than a previous version of the multilevel randomised response method that ignores the presence of cheating behaviours in the direct questioning stage.</p>\u0000 </div>","PeriodicalId":14479,"journal":{"name":"International Statistical Review","volume":"94 1","pages":"202-220"},"PeriodicalIF":1.8,"publicationDate":"2026-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147683547","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":"Handling Out-of-Sample Areas to Estimate the Unemployment Rate at Local Labour Market Areas in Italy","authors":"Roberto Benedetti,&nbsp;Federica Piersimoni,&nbsp;Monica Pratesi,&nbsp;Nicola Salvati,&nbsp;Thomas Suesse","doi":"10.1111/insr.12596","DOIUrl":"10.1111/insr.12596","url":null,"abstract":"<p>Unemployment rate estimates for small areas are used to efficiently support the distribution of services and the allocation of resources, grants and funding. A Fay–Herriot type model is the most used tool to obtain these estimates. Under this approach out-of-sample areas require some synthetic estimates. As the geographical context is extremely important for analysing local economies, in this paper, we allow for area random effects to be spatially correlated. The spatial model parameters are estimated by a marginal likelihood method and are used to predict in-sample as well as out-of-sample areas. Extensive simulation experiments are used to assess the impact of the auto-regression parameter and of the rate of out-of-sample areas on the performance of this approach. The paper concludes with an illustrative application on real data from the Italian Labour Force Survey in which the estimation of the unemployment rate in each Local Labour Market Area is addressed.</p>","PeriodicalId":14479,"journal":{"name":"International Statistical Review","volume":"94 1","pages":"140-162"},"PeriodicalIF":1.8,"publicationDate":"2026-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/insr.12596","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142182405","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":"Discussion to the paper ‘Robust Distance Covariance’","authors":"Klaus Nordhausen,&nbsp;Una Radojičić","doi":"10.1111/insr.70013","DOIUrl":"https://doi.org/10.1111/insr.70013","url":null,"abstract":"&lt;p&gt;We would like to thank S. Leyder, J. Raymaekers, and P. Rousseeuw for their insightful and well-written article ‘Robust Distance Covariance’. The paper provides a clear and comprehensive overview of distance covariance and related concepts and derives their influence functions and breakdown points. It is shown that, depending on parameter choices, classical distance covariance can exhibit a degree of robustness, although it still falls somewhat short in this regard.&lt;/p&gt;&lt;p&gt;To address this limitation, the authors introduce a novel robust version of distance covariance. By transforming the data into a higher-dimensional bounded domain, their method achieves a high breakdown point while preserving the desirable property that a zero value of distance covariance implies independence between the random elements involved.&lt;/p&gt;&lt;p&gt;Historically, the robust statistics literature has paid limited attention to the properties of statistical methods in settings where independence is the central concept. This may be attributed to the dominance of elliptical models, where independence is typically not a relevant notion. However, the growing popularity of models such as the independent component model (see Nordhausen and Oja &lt;span&gt;2018&lt;/span&gt;) has increasingly motivated the investigation of robust estimation techniques in scenarios where independence plays a critical role (Nordhausen and Tyler &lt;span&gt;2015&lt;/span&gt;).&lt;/p&gt;&lt;p&gt;These investigations have revealed that many scatter functionals fail to return zeros at the appropriate entries when components are independent, especially in the presence of asymmetry. As shown in Oja et al. (&lt;span&gt;2006&lt;/span&gt;) and Nordhausen and Tyler (&lt;span&gt;2015&lt;/span&gt;), a fruitful strategy is to symmetrise the data and operate on pairwise differences—a principle that is also inherent in the concept of distance covariance, as further highlighted in Raymaekers and Rousseeuw (&lt;span&gt;2025&lt;/span&gt;).&lt;/p&gt;&lt;p&gt;In this discussion, we are particularly interested in the application of (robust) generalized distance covariance in multivariate contexts, extending beyond the primarily bivariate focus of S. Leyder, J. Raymaekers, and P. Rousseeuw's article. At first glance, it may seem unusual that, regardless of the dimensionality of the vectors considered, (robust) generalized distance covariance returns a scalar rather than a matrix. From a multivariate perspective, this naturally invites consideration of the method within the framework of projection pursuit.&lt;/p&gt;&lt;p&gt;The concept of projection pursuit (PP) dates back several decades, with the term itself introduced by Friedman and Tukey (&lt;span&gt;1974&lt;/span&gt;). The fundamental idea is to apply a (typically univariate) measure of ‘information’ to multivariate data by identifying linear combinations of the variables that maximise this measure. The resulting directions are considered the most informative components of the data.&lt;/p&gt;&lt;p&gt;A wide variety of information measures have been proposed, and many well-known statisti","PeriodicalId":14479,"journal":{"name":"International Statistical Review","volume":"94 1","pages":"34-40"},"PeriodicalIF":1.8,"publicationDate":"2026-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/insr.70013","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147683464","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":"Variance Matrix Priors for Dirichlet Process Mixture Models With Gaussian Kernels","authors":"Wei Jing,&nbsp;Michail Papathomas,&nbsp;Silvia Liverani","doi":"10.1111/insr.12595","DOIUrl":"https://doi.org/10.1111/insr.12595","url":null,"abstract":"<p>Bayesian mixture modelling is widely used for density estimation and clustering. The Dirichlet process mixture model (DPMM) is the most popular Bayesian non-parametric mixture modelling approach. In this manuscript, we study the choice of prior for the variance or precision matrix when Gaussian kernels are adopted. Typically, in the relevant literature, the assessment of mixture models is done by considering observations in a space of only a handful of dimensions. Instead, we are concerned with more realistic problems of higher dimensionality, in a space of up to 20 dimensions. We observe that the choice of prior is increasingly important as the dimensionality of the problem increases. After identifying certain undesirable properties of standard priors in problems of higher dimensionality, we review and implement possible alternative priors. The most promising priors are identified, as well as other factors that affect the convergence of MCMC samplers. Our results show that the choice of prior is critical for deriving reliable posterior inferences. This manuscript offers a thorough overview and comparative investigation into possible priors, with detailed guidelines for their implementation. Although our work focuses on the use of the DPMM in clustering, it is also applicable to density estimation.</p>","PeriodicalId":14479,"journal":{"name":"International Statistical Review","volume":"94 1","pages":"163-187"},"PeriodicalIF":1.8,"publicationDate":"2026-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/insr.12595","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147683719","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":"Rejoinder","authors":"Sarah Leyder,&nbsp;Jakob Raymaekers,&nbsp;Peter J. Rousseeuw","doi":"10.1111/insr.70010","DOIUrl":"https://doi.org/10.1111/insr.70010","url":null,"abstract":"","PeriodicalId":14479,"journal":{"name":"International Statistical Review","volume":"94 1","pages":"53-60"},"PeriodicalIF":1.8,"publicationDate":"2026-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147683849","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":"Flexible Multivariate Mixture Models: A Comprehensive Approach for Modeling Mixtures of Non-Identical Distributions","authors":"Samyajoy Pal,&nbsp;Christian Heumann","doi":"10.1111/insr.12593","DOIUrl":"10.1111/insr.12593","url":null,"abstract":"<div>\u0000 \u0000 <p>The mixture models are widely used to analyze data with cluster structures and the mixture of Gaussians is most common in practical applications. The use of mixtures involving other multivariate distributions, like the multivariate skew normal and multivariate generalised hyperbolic, is also found in the literature. However, in all such cases, only the mixtures of identical distributions are used to form a mixture model. We present an innovative and versatile approach for constructing mixture models involving identical and non-identical distributions combined in all conceivable permutations (e.g. a mixture of multivariate skew normal and multivariate generalised hyperbolic). We also establish any conventional mixture model as a distinctive particular case of our proposed framework. The practical efficacy of our model is shown through its application to both simulated and real-world data sets. Our comprehensive and flexible model excels at recognising inherent patterns and accurately estimating parameters.</p>\u0000 </div>","PeriodicalId":14479,"journal":{"name":"International Statistical Review","volume":"94 1","pages":"61-96"},"PeriodicalIF":1.8,"publicationDate":"2026-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141933219","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}