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Confidence set for mixture order selection 混合顺序选择的置信度
IF 0.7 4区 数学
Statistics & Probability Letters Pub Date : 2025-07-28 DOI: 10.1016/j.spl.2025.110509
Alessandro Casa, Davide Ferrari
{"title":"Confidence set for mixture order selection","authors":"Alessandro Casa,&nbsp;Davide Ferrari","doi":"10.1016/j.spl.2025.110509","DOIUrl":"10.1016/j.spl.2025.110509","url":null,"abstract":"<div><div>A fundamental challenge in approximating an unknown density using finite Gaussian mixture models is selecting the number of mixture components, also known as order. Traditional approaches choose a single best model using information criteria. However, often models with different orders yield similar fits, leading to substantial model selection uncertainty and making it challenging to identify the optimal number of components. In this paper, we introduce the Model Selection Confidence Set (MSCS) for order selection in Gaussian mixtures – a set-valued estimator that, with a predefined confidence level, includes the true mixture order across repeated samples. Rather than selecting a single model, our MSCS identifies all plausible orders by determining whether each candidate model is at least as plausible as the best-selected one, using a screening based on a penalized likelihood ratio statistic. We provide theoretical guarantees for asymptotic coverage, and demonstrate its practical advantages through simulations and real data analysis.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"226 ","pages":"Article 110509"},"PeriodicalIF":0.7,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144724685","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 mixture model for skewed mixed-type data 偏斜混合型数据的混合模型
IF 0.7 4区 数学
Statistics & Probability Letters Pub Date : 2025-07-25 DOI: 10.1016/j.spl.2025.110507
Eman M.S. Alamer , Michael P.B. Gallaugher , Paul D. McNicholas
{"title":"A mixture model for skewed mixed-type data","authors":"Eman M.S. Alamer ,&nbsp;Michael P.B. Gallaugher ,&nbsp;Paul D. McNicholas","doi":"10.1016/j.spl.2025.110507","DOIUrl":"10.1016/j.spl.2025.110507","url":null,"abstract":"<div><div>Many approaches exist for clustering categorical or continuous data. However, there are few options for mixed-type data, especially when the clusters exhibit skewness and/or heavy tails in the continuous variables. A model-based clustering approach is proposed to help address this gap.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"226 ","pages":"Article 110507"},"PeriodicalIF":0.7,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144749006","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
An appraisal of approximation error in variational inference 变分推理中近似误差的评价
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-07-25 DOI: 10.1016/j.spl.2025.110505
Silvelyn Zwanzig , Rauf Ahmad
{"title":"An appraisal of approximation error in variational inference","authors":"Silvelyn Zwanzig ,&nbsp;Rauf Ahmad","doi":"10.1016/j.spl.2025.110505","DOIUrl":"10.1016/j.spl.2025.110505","url":null,"abstract":"<div><div>We show that in a linear model setting, the minimization problem in variational inference pertains to approximation error under suitable prior. We further show that the choice of prior preferred by the approximating member in mean-field family trades itself off with model assumptions. To demonstrate this, we also prove a result of general interest for linear algebra.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"226 ","pages":"Article 110505"},"PeriodicalIF":0.9,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144713341","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 completion of counterexamples to the classical central limit theorem for triplewise independent and identically distributed random variables 三独立同分布随机变量经典中心极限定理的反例完成
IF 0.7 4区 数学
Statistics & Probability Letters Pub Date : 2025-07-25 DOI: 10.1016/j.spl.2025.110508
Martin Raič
{"title":"A completion of counterexamples to the classical central limit theorem for triplewise independent and identically distributed random variables","authors":"Martin Raič","doi":"10.1016/j.spl.2025.110508","DOIUrl":"10.1016/j.spl.2025.110508","url":null,"abstract":"<div><div>By the Lindeberg–Lévy central limit theorem, standardized partial sums of a sequence of mutually independent and identically distributed random variables converge in law to the standard normal distribution. It is known that mutual independence cannot be relaxed to pairwise independence, nor even to triplewise independence. Counterexamples have been constructed for most marginal distributions: a recent construction works under a condition which excludes certain probability distributions with atomic parts, in particular almost all distributions on a fixed finite set. In the present paper, we show that this condition can be lifted: for any probability distribution <span><math><mi>F</mi></math></span> on the real line, which has finite variance and is not concentrated in a single point, there exists a sequence of triplewise independent random variables with distribution <span><math><mi>F</mi></math></span>, such that its standardized partial sums converge in law to a distribution which is not normal. There is also scope for extension to <span><math><mi>k</mi></math></span>-tuplewise independence.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"226 ","pages":"Article 110508"},"PeriodicalIF":0.7,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144724686","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
Nested nearly orthogonal Latin hypercube designs for many design columns 许多设计列的嵌套近正交拉丁超立方体设计
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-07-17 DOI: 10.1016/j.spl.2025.110503
Xinxin Xia , Yishan Zhou , Zijian Han
{"title":"Nested nearly orthogonal Latin hypercube designs for many design columns","authors":"Xinxin Xia ,&nbsp;Yishan Zhou ,&nbsp;Zijian Han","doi":"10.1016/j.spl.2025.110503","DOIUrl":"10.1016/j.spl.2025.110503","url":null,"abstract":"<div><div>Nested Latin hypercube designs are widely employed for conducting multiple computer experiments with varying levels of fidelity. In the context of polynomial function models, achieving orthogonality is particularly important, as it enables uncorrelated estimation of linear effects under a first-order model. Therefore, maintaining low inter-factor correlation is a highly desirable property in design construction. In this paper, we propose a novel method for constructing nested nearly orthogonal Latin hypercube designs with flexible design columns and low inter-factor correlations. Comparative studies with existing nested Latin hypercube designs demonstrate that the proposed designs achieve lower inter-factor correlations and require fewer runs, making them more efficient and cost-effective for practical applications.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"226 ","pages":"Article 110503"},"PeriodicalIF":0.9,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144654821","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
On weak convergence of Gaussian conditional distributions 高斯条件分布的弱收敛性
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-07-17 DOI: 10.1016/j.spl.2025.110497
Sarah Lumpp , Mathias Drton
{"title":"On weak convergence of Gaussian conditional distributions","authors":"Sarah Lumpp ,&nbsp;Mathias Drton","doi":"10.1016/j.spl.2025.110497","DOIUrl":"10.1016/j.spl.2025.110497","url":null,"abstract":"<div><div>Weak convergence of joint distributions generally does not imply convergence of conditional distributions. In particular, conditional distributions need not converge when joint Gaussian distributions converge to a singular Gaussian limit. Algebraically, this is due to the fact that at singular covariance matrices, Schur complements are not continuous functions of the matrix entries. Our results lay out special conditions under which convergence of Gaussian conditional distributions nevertheless occurs, and we exemplify how this allows one to reason about conditional independence in a new class of graphical models.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"226 ","pages":"Article 110497"},"PeriodicalIF":0.9,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144662947","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
Ergodicity of the stochastic Landau–Lifshitz–Bloch equation with multiplicative and additive noise 具有乘性和加性噪声的随机Landau-Lifshitz-Bloch方程的遍历性
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-07-15 DOI: 10.1016/j.spl.2025.110502
Mingli Hong , Zhaoyang Qiu
{"title":"Ergodicity of the stochastic Landau–Lifshitz–Bloch equation with multiplicative and additive noise","authors":"Mingli Hong ,&nbsp;Zhaoyang Qiu","doi":"10.1016/j.spl.2025.110502","DOIUrl":"10.1016/j.spl.2025.110502","url":null,"abstract":"<div><div>We study the ergodicity in <span><math><mrow><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup><mrow><mo>(</mo><mi>D</mi><mo>)</mo></mrow></mrow></math></span> of stochastic Landau–Lifshitz–Bloch equation evolving in either smooth bounded domains or unbounded domains, perturbed by both linear multiplicative and additive noises. Such noise is consistent with the fluctuation–dissipation theorem, which can be used to deduce a Boltzmann distribution valid for the full range of temperatures. We find that an exponential moment could be established in regularity space even for the multiplicative noise case. Then, based on it, we prove the exponential ergodicity.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"226 ","pages":"Article 110502"},"PeriodicalIF":0.9,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144654820","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
Asymptotics for the ruin probability of a bidimensional renewal risk model with dependent main claims and delayed claims 具有依赖主索赔和延迟索赔的二维续期风险模型破产概率的渐近性
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-07-12 DOI: 10.1016/j.spl.2025.110501
Yiqiao Jia, Mingyu Jiang, Dongya Cheng
{"title":"Asymptotics for the ruin probability of a bidimensional renewal risk model with dependent main claims and delayed claims","authors":"Yiqiao Jia,&nbsp;Mingyu Jiang,&nbsp;Dongya Cheng","doi":"10.1016/j.spl.2025.110501","DOIUrl":"10.1016/j.spl.2025.110501","url":null,"abstract":"<div><div>This paper considers a bidimensional renewal risk model incorporating the dependent main claims and delayed claims, where both the main claims and delayed claims are long-tailed and dominatedly-varying-tailed. It is assumed that both the main claim pairs and the corresponding delayed claim pairs follow the strongly asymptotic independence structure. For this model, a precise asymptotic formula for the finite-time ruin probability is established when the initial surpluses tend to infinity, thereby extending some recent findings in the literature.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"226 ","pages":"Article 110501"},"PeriodicalIF":0.9,"publicationDate":"2025-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144654819","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
Distorted expectiles risk measure and LP formulation 扭曲预期物的风险度量与LP的制定
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-07-11 DOI: 10.1016/j.spl.2025.110496
Sally Giuseppe Arcidiacono, Damiano Rossello
{"title":"Distorted expectiles risk measure and LP formulation","authors":"Sally Giuseppe Arcidiacono,&nbsp;Damiano Rossello","doi":"10.1016/j.spl.2025.110496","DOIUrl":"10.1016/j.spl.2025.110496","url":null,"abstract":"<div><div>Given a concave distortion function, we provide a dual representation of the expectiles based on rank-dependent expected utility theory. With possible application to portfolio management in mind, we also derive an LP formulation of the related optimization problem.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"226 ","pages":"Article 110496"},"PeriodicalIF":0.9,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144604605","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
Normal approximations for sequences with the property of strong N-demimartingale differences 具有强n -二分差性质的序列的正态逼近
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-07-09 DOI: 10.1016/j.spl.2025.110498
Xiaomei Zhang , Jingjun Guo
{"title":"Normal approximations for sequences with the property of strong N-demimartingale differences","authors":"Xiaomei Zhang ,&nbsp;Jingjun Guo","doi":"10.1016/j.spl.2025.110498","DOIUrl":"10.1016/j.spl.2025.110498","url":null,"abstract":"<div><div>We consider a class of dependent random variable sequences with the property of strong <span><math><mi>N</mi></math></span>-demimartingale differences and provide examples to illustrate certain characteristics of these sequences. An upper bound is established for Zolotarev ideal metric between this class of sequences and a normal random variable, thereby leading to the derivation of a central limit theorem for such dependent structure. Additionally, we present numerical analyses to support our findings.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"226 ","pages":"Article 110498"},"PeriodicalIF":0.9,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144604612","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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