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Discussion of “Mode-based estimation of the center of symmetry” 关于“基于模态的对称中心估计”的讨论
IF 0.6 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2025-07-31 DOI: 10.1007/s10463-025-00944-x
Juan Carlos Pardo-Fernández
{"title":"Discussion of “Mode-based estimation of the center of symmetry”","authors":"Juan Carlos Pardo-Fernández","doi":"10.1007/s10463-025-00944-x","DOIUrl":"10.1007/s10463-025-00944-x","url":null,"abstract":"","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":"77 5","pages":"723 - 725"},"PeriodicalIF":0.6,"publicationDate":"2025-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144923353","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Discussion of “Mode-based estimation of the center of symmetry” 关于“基于模态的对称中心估计”的讨论
IF 0.6 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2025-07-31 DOI: 10.1007/s10463-025-00943-y
Hideitsu Hino
{"title":"Discussion of “Mode-based estimation of the center of symmetry”","authors":"Hideitsu Hino","doi":"10.1007/s10463-025-00943-y","DOIUrl":"10.1007/s10463-025-00943-y","url":null,"abstract":"","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":"77 5","pages":"719 - 721"},"PeriodicalIF":0.6,"publicationDate":"2025-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144923282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Mode-based estimation of the center of symmetry 基于模态的对称中心估计
IF 0.6 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2025-07-31 DOI: 10.1007/s10463-025-00942-z
José E. Chacón, Javier Fernández Serrano
{"title":"Mode-based estimation of the center of symmetry","authors":"José E. Chacón,&nbsp;Javier Fernández Serrano","doi":"10.1007/s10463-025-00942-z","DOIUrl":"10.1007/s10463-025-00942-z","url":null,"abstract":"<div><p>In the mean-median-mode triad of univariate centrality measures, the mode has been overlooked for estimating the center of symmetry in continuous and unimodal settings. This paper expands on the connection between kernel mode estimators and M-estimators for location, bridging the gap between the nonparametrics and robust statistics communities. The variance of modal estimators is studied in terms of a bandwidth parameter, establishing conditions for an optimal solution that outperforms the household sample mean. A purely nonparametric approach is adopted, modeling heavy-tailedness through regular variation. The results lead to an estimator proposal that includes a novel one-parameter family of kernels with compact support, offering extra robustness and efficiency. The effectiveness and versatility of the new method are demonstrated in a real-world case study and a thorough simulation study, comparing favorably to traditional and more competitive alternatives. Several myths about the mode are clarified along the way, reopening the quest for flexible and efficient nonparametric estimators.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":"77 5","pages":"685 - 717"},"PeriodicalIF":0.6,"publicationDate":"2025-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144923283","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Rejoinder to the discussion of “Mode-based estimation of the center of symmetry” 对“基于模态的对称中心估计”讨论的回答
IF 0.6 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2025-07-31 DOI: 10.1007/s10463-025-00945-w
José E. Chacón, Javier Fernández Serrano
{"title":"Rejoinder to the discussion of “Mode-based estimation of the center of symmetry”","authors":"José E. Chacón,&nbsp;Javier Fernández Serrano","doi":"10.1007/s10463-025-00945-w","DOIUrl":"10.1007/s10463-025-00945-w","url":null,"abstract":"","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":"77 5","pages":"727 - 730"},"PeriodicalIF":0.6,"publicationDate":"2025-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144923354","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Central limit theorems for vector-valued composite functionals with smoothing and applications 具有平滑的向量值复合泛函的中心极限定理及其应用
IF 0.6 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2025-07-21 DOI: 10.1007/s10463-025-00934-z
Huihui Chen, Darinka Dentcheva, Yang Lin, Gregory J. Stock
{"title":"Central limit theorems for vector-valued composite functionals with smoothing and applications","authors":"Huihui Chen,&nbsp;Darinka Dentcheva,&nbsp;Yang Lin,&nbsp;Gregory J. Stock","doi":"10.1007/s10463-025-00934-z","DOIUrl":"10.1007/s10463-025-00934-z","url":null,"abstract":"<div><p>This paper focuses on vector-valued composite functionals, which may be nonlinear in probability. Our goal is establishing central limit theorems for these functionals when employed by mixed estimators. Our study is relevant to the evaluation and comparison of risk in decision-making contexts and extends to functionals that arise in machine learning. A generalized family of composite risk functionals is presented, which encompasses coherent risk measures, including systemic risk. The paper makes two main contributions. First, we analyze vector-valued functionals and provide a framework for evaluating high-dimensional risks. This enables comparison of multiple risk measures and supports estimation and asymptotic analysis of systemic risk and its optimal value in decision-making. Second, we derive new central limit theorems for optimized composite functionals using mixed estimators, including empirical and smoothed types. We give verifiable conditions for central limit formulae and demonstrate their applicability to several risk measures.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":"77 5","pages":"821 - 852"},"PeriodicalIF":0.6,"publicationDate":"2025-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144923247","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Posterior contraction rate and asymptotic Bayes optimality for one group global–local shrinkage priors in sparse normal means problem 稀疏正态均值问题中一组全局-局部收缩先验的后验收缩率和渐近贝叶斯最优性
IF 0.6 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2025-06-24 DOI: 10.1007/s10463-025-00932-1
Sayantan Paul, Arijit Chakrabarti
{"title":"Posterior contraction rate and asymptotic Bayes optimality for one group global–local shrinkage priors in sparse normal means problem","authors":"Sayantan Paul,&nbsp;Arijit Chakrabarti","doi":"10.1007/s10463-025-00932-1","DOIUrl":"10.1007/s10463-025-00932-1","url":null,"abstract":"<div><p>We study inference on the mean vector of the normal means model in sparse asymptotic settings when it is modelled by broad classes of one-group global–local continuous shrinkage priors. We prove that the resulting posterior distributions contract around the truth at a near minimax rate with respect to squared <span>(L_2)</span> loss when the global shrinkage parameter is estimated in empirical Bayesian ways or arbitrary priors supported on some appropriate interval are assigned to it. We then employ an intuitive multiple testing rule (using full Bayes treatment with global–local priors) in a problem of simultaneous testing (with additive misclassification loss) for the components of the mean assuming they are iid from a two-groups prior. In a first result of its kind, risk of our testing rule is shown to asymptotically match (up to a constant) that of the optimal rule in the two-groups setting. </p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":"77 5","pages":"787 - 819"},"PeriodicalIF":0.6,"publicationDate":"2025-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144923235","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Selection-bias-adjusted inference for the bivariate normal distribution under soft-threshold sampling 软阈值抽样下二元正态分布的选择偏差调整推理
IF 0.6 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2025-05-02 DOI: 10.1007/s10463-025-00925-0
Joseph B. Lang
{"title":"Selection-bias-adjusted inference for the bivariate normal distribution under soft-threshold sampling","authors":"Joseph B. Lang","doi":"10.1007/s10463-025-00925-0","DOIUrl":"10.1007/s10463-025-00925-0","url":null,"abstract":"<div><p>The problem of estimating parameters and predicting outcomes of a bivariate Normal distribution is more challenging when, owing to data-dependent selection (or missingness or dropout), the available data are not a representative sample of bivariate realizations. This problem is addressed using an observation model that is induced by a combination of a multivariate Normal “science” model and a realistic “soft-threshold selection” model with unknown truncation point. This observation model, which is expressed using an intuitive selection subset notation, is a generalization of existing “hard-threshold” models. It affords simple-to-compute selection-bias-adjusted estimates of both the regression (conditional mean) parameters and the bivariate correlation. In addition, a simple bootstrap approach for computing both confidence and prediction intervals in the soft-threshold selection setting is described. Simulation results are promising. To motivate this research, two illustrative examples describe a setting where selection bias is an issue of concern.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":"77 4","pages":"597 - 625"},"PeriodicalIF":0.6,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145141921","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 signed-rank estimator for nonlinear regression models when covariates and errors are dependent 当协变量和误差相关时非线性回归模型的带符号秩估计
IF 0.6 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2025-04-30 DOI: 10.1007/s10463-025-00929-w
Hira L. Koul, Palaniappan Vellaisamy
{"title":"A signed-rank estimator for nonlinear regression models when covariates and errors are dependent","authors":"Hira L. Koul,&nbsp;Palaniappan Vellaisamy","doi":"10.1007/s10463-025-00929-w","DOIUrl":"10.1007/s10463-025-00929-w","url":null,"abstract":"<div><p>This paper contains the proof of the asymptotic uniform linearity of a sequence of simple linear signed-rank statistics based on the residuals of a class of nonlinear parametric regression models, where regression errors are possibly dependent on the covariates. This result in turn is used to prove the asymptotic normality of a signed rank estimator of the regression parameter vector in the given nonlinear regression model where covariates and regression errors are dependent and in the errors in variables linear regression model, when the distributions of the covariates and measurement errors are known.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":"77 4","pages":"563 - 596"},"PeriodicalIF":0.6,"publicationDate":"2025-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145145630","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
The family of multivariate beta copulas revisited 重新审视多元联结函数族
IF 0.6 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2025-04-28 DOI: 10.1007/s10463-025-00931-2
Enagnon Narcisse Agbangla, Jean-François Quessy, Louis-Paul Rivest
{"title":"The family of multivariate beta copulas revisited","authors":"Enagnon Narcisse Agbangla,&nbsp;Jean-François Quessy,&nbsp;Louis-Paul Rivest","doi":"10.1007/s10463-025-00931-2","DOIUrl":"10.1007/s10463-025-00931-2","url":null,"abstract":"<div><p>This article sheds new lights on the family of multivariate beta copulas that arises as the dependence structures of the multivariate generalized beta distribution of the second type. In particular, simple formulas for the computation of Kendall’s measure of association are derived and the asymmetry properties are investigated. Also, the multivariate extreme-value attractor of the beta copula is identified and it is shown that the beta family is closed under conditioning and belongs to the class of one-factor copulas. The sampling properties of the rank-based maximum-likelihood estimator are investigated with simulations and the usefulness of the beta copulas for the modeling of multivariate datasets is illustrated on triathlon data.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":"77 5","pages":"757 - 786"},"PeriodicalIF":0.6,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144923222","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Offline minimax Q-function learning for undiscounted indefinite-horizon MDPs 未折现不定视界mdp的离线极大极小q函数学习
IF 0.6 4区 数学
Annals of the Institute of Statistical Mathematics Pub Date : 2025-04-21 DOI: 10.1007/s10463-025-00924-1
Fengying Li, Yuqiang Li, Xianyi Wu, Wei Bai
{"title":"Offline minimax Q-function learning for undiscounted indefinite-horizon MDPs","authors":"Fengying Li,&nbsp;Yuqiang Li,&nbsp;Xianyi Wu,&nbsp;Wei Bai","doi":"10.1007/s10463-025-00924-1","DOIUrl":"10.1007/s10463-025-00924-1","url":null,"abstract":"<div><p>This work considers the offline evaluation problem for indefinite-horizon Markov Decision Processes. A minimax Q-function learning algorithm is proposed, which, instead of i.i.d. tuples <span>((s,a,s',r))</span>, evaluates undiscounted expected return based by i.i.d. trajectories truncated at a given time step. The confidence error bounds are developed. Experiments using Open AI’s Cart Pole environment are employed to demonstrate the algorithm.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":"77 4","pages":"535 - 562"},"PeriodicalIF":0.6,"publicationDate":"2025-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145144486","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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