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Lower bounds for density estimation on symmetric spaces
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-03-31 DOI: 10.1016/j.spl.2025.110416
Dena Marie Asta
{"title":"Lower bounds for density estimation on symmetric spaces","authors":"Dena Marie Asta","doi":"10.1016/j.spl.2025.110416","DOIUrl":"10.1016/j.spl.2025.110416","url":null,"abstract":"<div><div>We prove that kernel density estimation on symmetric spaces of non-compact type, whose <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-risk was bounded above in previous work (Asta, 2021), in fact achieves a minimax rate of convergence. With this result, the story for kernel density estimation on all symmetric spaces is completed. The idea in adapting the proof for Euclidean space is to suitably abstract vector space operations on Euclidean space to both actions of symmetric groups and reparametrizations of Helgason–Fourier transforms and to use the fact that the exponential map for symmetric spaces of non-compact type defines a diffeomorphism.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"223 ","pages":"Article 110416"},"PeriodicalIF":0.9,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143759730","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Posterior model consistency in high-dimensional Bayesian variable selection with arbitrary priors
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-03-28 DOI: 10.1016/j.spl.2025.110415
Min Hua , Gyuhyeong Goh
{"title":"Posterior model consistency in high-dimensional Bayesian variable selection with arbitrary priors","authors":"Min Hua ,&nbsp;Gyuhyeong Goh","doi":"10.1016/j.spl.2025.110415","DOIUrl":"10.1016/j.spl.2025.110415","url":null,"abstract":"<div><div>In the context of Bayesian regression modeling, posterior model consistency provides frequentist validation for Bayesian variable selection. A question that has long been open is whether posterior model consistency holds under arbitrary priors when high-dimensional variable selection is performed. In this paper, we aim to give an answer by establishing sufficient conditions for priors under which the posterior model distribution converges to a degenerate distribution at the true model. Our framework considers high-dimensional regression settings where the number of potential predictors grows at a rate faster than the sample size. We demonstrate that a wide selection of priors satisfy the conditions that we establish in this paper.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"223 ","pages":"Article 110415"},"PeriodicalIF":0.9,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143734875","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 impact of contamination and correlated design on the Lasso: An average case analysis
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-03-28 DOI: 10.1016/j.spl.2025.110417
Stanislav Minsker , Yiqiu Shen
{"title":"The impact of contamination and correlated design on the Lasso: An average case analysis","authors":"Stanislav Minsker ,&nbsp;Yiqiu Shen","doi":"10.1016/j.spl.2025.110417","DOIUrl":"10.1016/j.spl.2025.110417","url":null,"abstract":"<div><div>We study the prediction problem in the context of the high-dimensional linear regression model. We focus on the practically relevant framework where a fraction of the linear measurements is corrupted while the columns of the design matrix can be moderately correlated. Our findings suggest that for most sparse signals, the Lasso estimator admits strong performance guarantees under more easily verifiable and less stringent assumptions on the design matrix compared to much of the existing literature.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"223 ","pages":"Article 110417"},"PeriodicalIF":0.9,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143759731","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
Solution to a generalized FBSDE with delay and anticipated terms and applications to control problem with time-varying delay
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-03-25 DOI: 10.1016/j.spl.2025.110414
Yuecai Han , Yuhang Li , Zheng Li
{"title":"Solution to a generalized FBSDE with delay and anticipated terms and applications to control problem with time-varying delay","authors":"Yuecai Han ,&nbsp;Yuhang Li ,&nbsp;Zheng Li","doi":"10.1016/j.spl.2025.110414","DOIUrl":"10.1016/j.spl.2025.110414","url":null,"abstract":"<div><div>In this paper, motivated by optimal control problem with time-varying delay, we study a type of generalized forward–backward stochastic differential equation. Both delay and anticipated terms appear in both forward equation and backward equation. The existence and uniqueness of the solution is obtained. As an application, the linear quadratic optimal control problem, where both state process and control process contain time-varying delay, is solved.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"223 ","pages":"Article 110414"},"PeriodicalIF":0.9,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143705736","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 novel approach for estimating multi-attribute Gaussian copula graphical models
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-03-24 DOI: 10.1016/j.spl.2025.110413
Lijie Li , Yang Yu , Wanfeng Liang , Feng Zou
{"title":"A novel approach for estimating multi-attribute Gaussian copula graphical models","authors":"Lijie Li ,&nbsp;Yang Yu ,&nbsp;Wanfeng Liang ,&nbsp;Feng Zou","doi":"10.1016/j.spl.2025.110413","DOIUrl":"10.1016/j.spl.2025.110413","url":null,"abstract":"<div><div>This paper considers estimating multi-attribute Gaussian copula graphical models where each node represents multivariate variables with rich meanings. A two-stage semiparametric method is proposed to achieve modeling flexibility and estimation robustness simultaneously by utilizing normal score transformation. We derive the consistency of the proposed estimator under the spectral norm, and establish the theoretical guarantees on sparsistency under some mild conditions. Simulation studies and a real data example are provided to demonstrate the empirical performance of the proposed method. We provide the complete code supporting this article at <span><span>https://github.com/JerryLi-Stat/Multi-attribute-GCGM</span><svg><path></path></svg></span>.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"222 ","pages":"Article 110413"},"PeriodicalIF":0.9,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143683346","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
Transportation cost inequalities for the stochastic Ginzburg–Landau equation driven by space–time white noises
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-03-24 DOI: 10.1016/j.spl.2025.110409
Beibei Zhang
{"title":"Transportation cost inequalities for the stochastic Ginzburg–Landau equation driven by space–time white noises","authors":"Beibei Zhang","doi":"10.1016/j.spl.2025.110409","DOIUrl":"10.1016/j.spl.2025.110409","url":null,"abstract":"<div><div>In this paper, we establish transportation cost inequalities for the solution of the stochastic complex Ginzburg–Landau equation driven by a space–time white noise on the spaces <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>]</mo></mrow><mo>×</mo><mi>D</mi><mo>)</mo></mrow></mrow></math></span> or <span><math><mrow><mi>C</mi><mrow><mo>(</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>]</mo></mrow><mo>;</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>D</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow></math></span>. The proof is based on the estimates of the nonlinear term.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"222 ","pages":"Article 110409"},"PeriodicalIF":0.9,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143696877","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 local long-time behaviour for continuous-time branching processes
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-03-24 DOI: 10.1016/j.spl.2025.110412
Liuyan Li , Junping Li
{"title":"The local long-time behaviour for continuous-time branching processes","authors":"Liuyan Li ,&nbsp;Junping Li","doi":"10.1016/j.spl.2025.110412","DOIUrl":"10.1016/j.spl.2025.110412","url":null,"abstract":"<div><div>Let <span><math><mrow><mo>{</mo><mi>Z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>;</mo><mi>t</mi><mo>≥</mo><mn>0</mn><mo>}</mo></mrow></math></span> be a continuous-time branching process. There is a normalizing function <span><math><msub><mrow><mi>γ</mi></mrow><mrow><mi>t</mi></mrow></msub></math></span> such that <span><math><mrow><mi>Z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><msub><mrow><mi>γ</mi></mrow><mrow><mi>t</mi></mrow></msub></mrow></math></span> converges almost surely to a random variable. In this paper, we obtain a local limit theorem for <span><math><mrow><mo>{</mo><mi>Z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>;</mo><mi>t</mi><mo>≥</mo><mn>0</mn><mo>}</mo></mrow></math></span>, which refers to the asymptotic behaviour of <span><math><mrow><mi>P</mi><mrow><mo>(</mo><mi>Z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><msub><mrow><mi>k</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>)</mo></mrow></mrow></math></span> with <span><math><mrow><munder><mrow><mo>lim</mo></mrow><mrow><mi>t</mi><mo>→</mo><mi>∞</mi></mrow></munder><msub><mrow><mi>k</mi></mrow><mrow><mi>t</mi></mrow></msub><msub><mrow><mi>γ</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>x</mi></mrow></math></span> and <span><math><mrow><mi>x</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>. This expands the existing results of the discrete-time branching processes.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"223 ","pages":"Article 110412"},"PeriodicalIF":0.9,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143715864","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
Weak limits of standardized sums of independent geometrically distributed random variables
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-03-23 DOI: 10.1016/j.spl.2025.110410
José A. Adell
{"title":"Weak limits of standardized sums of independent geometrically distributed random variables","authors":"José A. Adell","doi":"10.1016/j.spl.2025.110410","DOIUrl":"10.1016/j.spl.2025.110410","url":null,"abstract":"<div><div>We consider standardized sums of independent geometrically distributed random variables whose failure probabilities approach the unity. We show that such sums converge in law to a random variable having an infinitely divisible distribution whose characteristic function depends on the values of the Riemann zeta function at integer arguments. This is motivated by a probabilistic representation of the Stirling numbers of the second kind.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"222 ","pages":"Article 110410"},"PeriodicalIF":0.9,"publicationDate":"2025-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143704104","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
Asymptotic normality of the Conditional Value-at-Risk based Pickands estimator
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-03-21 DOI: 10.1016/j.spl.2025.110411
Yizhou Li , Paweł Polak
{"title":"Asymptotic normality of the Conditional Value-at-Risk based Pickands estimator","authors":"Yizhou Li ,&nbsp;Paweł Polak","doi":"10.1016/j.spl.2025.110411","DOIUrl":"10.1016/j.spl.2025.110411","url":null,"abstract":"<div><div>We show weak convergence of the empirical Conditional Value-at-Risk (CVaR) in functional space and the asymptotic normality of the CVaR-based Pickands estimator from Chen (2021). These results demonstrate that the CVaR-based estimator has significantly lower asymptotic variance than analogous VaR-based constructions.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"223 ","pages":"Article 110411"},"PeriodicalIF":0.9,"publicationDate":"2025-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143704048","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
Construction of designs with space-filling and orthogonal property
IF 0.9 4区 数学
Statistics & Probability Letters Pub Date : 2025-03-19 DOI: 10.1016/j.spl.2025.110408
Min Li , Yuan Feng , Xiao Wang , Weiping Zhou
{"title":"Construction of designs with space-filling and orthogonal property","authors":"Min Li ,&nbsp;Yuan Feng ,&nbsp;Xiao Wang ,&nbsp;Weiping Zhou","doi":"10.1016/j.spl.2025.110408","DOIUrl":"10.1016/j.spl.2025.110408","url":null,"abstract":"<div><div>Space-filling designs are widely used in computer experiments, but their construction presents significant challenges. This paper introduces novel methods for generating maximin distance Latin hypercube designs (LHDs) and space-filling balanced designs with a slice structure, removing the reliance on computational searches. We also offer a simple yet effective approach to constructing sliced Latin hypercube designs (SLHDs), which achieve space-filling in each slice and maintain good orthogonality and stratification properties across the entire design. The resulting designs are more space-filling than existing designs.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"222 ","pages":"Article 110408"},"PeriodicalIF":0.9,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143683335","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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