Statistics & Probability Letters最新文献

{"title":"Spatial local linear quantile regression under association","authors":"Xin-Yi Xu ,&nbsp;Jiang-Feng Wang ,&nbsp;Kang Hu ,&nbsp;Shan He ,&nbsp;Yu Xia","doi":"10.1016/j.spl.2025.110573","DOIUrl":"10.1016/j.spl.2025.110573","url":null,"abstract":"<div><div>This paper investigates the asymptotic properties of local linear quantile regression estimators for spatial data generated by strictly stationary and associated spatial processes <span><math><mrow><mo>{</mo><mrow><mo>(</mo><msub><mrow><mi>Y</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>)</mo></mrow><mo>,</mo><mi>i</mi><mo>∈</mo><msup><mrow><mi>Z</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>}</mo></mrow></math></span>. We study local linear estimators for both the conditional quantile function <span><math><mrow><msub><mrow><mi>q</mi></mrow><mrow><mi>p</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> and its first-order partial derivatives. Under appropriate regularity conditions, we derive the Bahadur representation for these estimators, which is utilized to establish their joint asymptotic normality. To assess finite-sample performance, we conduct Monte Carlo simulations in a two-dimensional space (<span><math><mrow><mi>N</mi><mo>=</mo><mn>2</mn></mrow></math></span>). The results demonstrate the applicability of the proposed estimators and confirm the theoretical asymptotic properties.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"228 ","pages":"Article 110573"},"PeriodicalIF":0.7,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145269905","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}

{"title":"Communication-efficient distributed robust variable selection for heterogeneous massive data","authors":"Hang Zou ,&nbsp;Yunlu Jiang","doi":"10.1016/j.spl.2025.110557","DOIUrl":"10.1016/j.spl.2025.110557","url":null,"abstract":"<div><div>We propose a communication-efficient distributed robust variable selection method using discounted exponential regression for massive data. Theoretical properties of the proposed method are demonstrated. Simulation studies and the application to flue gas emission data illustrate the effectiveness of our approach.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"228 ","pages":"Article 110557"},"PeriodicalIF":0.7,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145321941","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}

{"title":"A note on the structure of the filtering recursion for finite HMMs","authors":"Dimitrios Katselis ,&nbsp;Boris I. Godoy ,&nbsp;Rodrigo Carvajal ,&nbsp;Juan C. Agüero","doi":"10.1016/j.spl.2025.110556","DOIUrl":"10.1016/j.spl.2025.110556","url":null,"abstract":"<div><div>The filter for a finite HMM at time <span><math><mi>k</mi></math></span> is expressed in terms of a stochastic matrix <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span>. We relate arbitrary pairs of rows in <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span> with the corresponding pairs of rows in the underlying <span><math><mrow><mo>(</mo><mi>k</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></math></span>-step transition matrix <span><math><mrow><msup><mrow><mi>P</mi></mrow><mrow><mrow><mo>(</mo><mi>k</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></mrow></msup><mo>=</mo><msup><mrow><mi>P</mi></mrow><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msup></mrow></math></span>.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"228 ","pages":"Article 110556"},"PeriodicalIF":0.7,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145160358","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}

{"title":"Multiple imputation of censored bivariate event-times via inverse transform and nonparametric Gibbs sampling","authors":"Daniela Angulo,&nbsp;Susan Murray","doi":"10.1016/j.spl.2025.110564","DOIUrl":"10.1016/j.spl.2025.110564","url":null,"abstract":"<div><div>Bivariate time-to-event data, subject to right censoring, frequently arise in medical research. This paper introduces a novel nonparametric multiple imputation (MI) procedure for analyzing censored bivariate time-to-event data. Our methodology offers a straightforward, easy-to-implement inverse transform MI method that effectively captures the joint distribution of bivariate random variables through the imputation of censored event-times.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"228 ","pages":"Article 110564"},"PeriodicalIF":0.7,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145269461","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}

{"title":"Optimal sub-Gaussian variance proxy for truncated Gaussian and exponential random variables","authors":"Mathias Barreto ,&nbsp;Olivier Marchal ,&nbsp;Julyan Arbel","doi":"10.1016/j.spl.2025.110555","DOIUrl":"10.1016/j.spl.2025.110555","url":null,"abstract":"<div><div>This paper establishes the optimal sub-Gaussian variance proxy for truncated Gaussian and truncated exponential random variables. The proofs are based initially on reducing each distribution to their standardized versions. Geometrically, for the normal distribution, our argument consists of fitting a parabola to another parabola-looking function, which emerges from its moment generating function. For the exponential case, we show that the optimal variance proxy is the unique solution to a pair of equations and then provide this solution explicitly. Moreover, we demonstrate that truncated Gaussian variables exhibit strict sub-Gaussian behavior if and only if they are symmetric, meaning their truncation is symmetric with respect to the mean. Conversely, truncated exponential variables are shown to never exhibit strict sub-Gaussianity.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"228 ","pages":"Article 110555"},"PeriodicalIF":0.7,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145120274","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}

{"title":"The eschewed sinh-arcsinh t distribution","authors":"M.C. Jones ,&nbsp;Arthur Pewsey","doi":"10.1016/j.spl.2025.110560","DOIUrl":"10.1016/j.spl.2025.110560","url":null,"abstract":"<div><div>Rosco et al. (2011) introduced and studied the sinh-arcsinh <span><math><mi>t</mi></math></span> (SAS-<span><math><mi>t</mi></math></span>) distribution. In this article, we introduce a modified version of that distribution which we call the eschewed sinh-arcsinh <span><math><mi>t</mi></math></span> (ESAS-<span><math><mi>t</mi></math></span>) distribution. The new proposal proves to be somewhat simpler than the former and, on balance, given the pros and cons listed in the article, we now recommend the ESAS-<span><math><mi>t</mi></math></span> distribution over the SAS-<span><math><mi>t</mi></math></span> distribution as the preferable version of a sinh-arcsinh <span><math><mi>t</mi></math></span> distribution.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"228 ","pages":"Article 110560"},"PeriodicalIF":0.7,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222581","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}

{"title":"Quasi-likelihood estimation for stochastic fractional heat equation","authors":"Yaqin Sun ,&nbsp;Jingqi Han ,&nbsp;Litan Yan","doi":"10.1016/j.spl.2025.110549","DOIUrl":"10.1016/j.spl.2025.110549","url":null,"abstract":"<div><div>By the quasi-likelihood method, in this note we consider parameter estimation of the fractional heat equation <span><span><span><math><mrow><mfrac><mrow><mi>∂</mi></mrow><mrow><mi>∂</mi><mi>t</mi></mrow></mfrac><mi>u</mi><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><msub><mrow><mi>Δ</mi></mrow><mrow><mi>α</mi></mrow></msub><mi>u</mi><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></mrow><mi>d</mi><mi>t</mi><mo>+</mo><mi>σ</mi><mover><mrow><mi>W</mi></mrow><mrow><mo>̇</mo></mrow></mover><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></mrow><mo>,</mo><mspace></mspace><mi>t</mi><mo>≥</mo><mn>0</mn><mo>,</mo><mi>x</mi><mo>∈</mo><mi>R</mi></mrow></math></span></span></span>with initial condition <span><math><mrow><mi>u</mi><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mn>0</mn></mrow></math></span>, where <span><math><mrow><mover><mrow><mi>W</mi></mrow><mrow><mo>̇</mo></mrow></mover><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> is a space–time white noise and <span><math><mrow><msub><mrow><mi>Δ</mi></mrow><mrow><mi>α</mi></mrow></msub><mo>=</mo><mo>−</mo><msup><mrow><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow></mrow><mrow><mi>α</mi><mo>/</mo><mn>2</mn></mrow></msup></mrow></math></span> is the fractional Laplacian with <span><math><mrow><mi>α</mi><mo>∈</mo><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>]</mo></mrow></mrow></math></span>. By using the quasi-likelihood method we obtain the estimator of <span><math><msup><mrow><mi>σ</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and give the asymptotic behaviors of the estimator provided that the spatial process <span><math><mrow><mi>x</mi><mo>↦</mo><mi>u</mi><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> can be observed at some discrete points <span><math><mrow><mo>{</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>=</mo><mi>j</mi><mi>h</mi><mo>,</mo><mi>j</mi><mo>=</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>n</mi><mo>}</mo></mrow></math></span> with <span><math><mrow><mi>h</mi><mo>=</mo><mi>h</mi><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow><mo>→</mo><mn>0</mn></mrow></math></span>, <span><math><mrow><mi>n</mi><msup><mrow><mi>h</mi></mrow><mrow><mn>1</mn><mo>+</mo><mi>γ</mi></mrow></msup><mo>→</mo><mi>R</mi><mo>≠</mo><mn>0</mn></mrow></math></span> for some <span><math><mrow><mn>0</mn><mo>≤</mo><mi>γ</mi><mo>&lt;</mo><mn>1</mn></mrow></math></span>, as <span><math><mrow><mi>n</mi><mo>→</mo><mi>∞</mi></mrow></math></span>.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"227 ","pages":"Article 110549"},"PeriodicalIF":0.7,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145060466","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}

{"title":"Random bridges in spaces of growing dimension","authors":"Bochen Jin","doi":"10.1016/j.spl.2025.110530","DOIUrl":"10.1016/j.spl.2025.110530","url":null,"abstract":"<div><div>We investigate the limiting behaviour of the path of random bridges treated as random sets in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> with the Euclidean metric and the dimension <span><math><mi>d</mi></math></span> increasing to infinity. The main result states that, in the square integrable case, the limit (in the Gromov–Hausdorff sense) is deterministic, namely, it is <span><math><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></math></span> equipped with the pseudo-metric <span><math><msqrt><mrow><mrow><mo>|</mo><mi>t</mi><mo>−</mo><mi>s</mi><mo>|</mo></mrow><mrow><mo>(</mo><mn>1</mn><mo>−</mo><mrow><mo>|</mo><mi>t</mi><mo>−</mo><mi>s</mi><mo>|</mo></mrow><mo>)</mo></mrow></mrow></msqrt></math></span>. We also show that, in the heavy-tailed case with summands regularly varying of order <span><math><mrow><mi>α</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>, the limiting metric space has a random metric derived from the bridge variant of a subordinator.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"227 ","pages":"Article 110530"},"PeriodicalIF":0.7,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144864937","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}

{"title":"Limit theorems for renewal processes with infinite mean interarrival time under random inspection","authors":"Diana Rauwolf","doi":"10.1016/j.spl.2025.110527","DOIUrl":"10.1016/j.spl.2025.110527","url":null,"abstract":"<div><div>Analogues to fundamental asymptotic relations in renewal theory are considered under the assumption that the time is a random variable and that the interarrival times have infinite mean. Limits are given for interarrival times with regularly varying tail and for sequences of parameters of the respective random-time distribution under mild conditions. An application to alternating renewal processes is shown.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"227 ","pages":"Article 110527"},"PeriodicalIF":0.7,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144878116","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}

{"title":"Dispersive and hazard rate orderings of parallel systems with exponential dependent components","authors":"Ghadah Alomani ,&nbsp;Anfal A. Alqefari ,&nbsp;Mohamed Kayid","doi":"10.1016/j.spl.2025.110514","DOIUrl":"10.1016/j.spl.2025.110514","url":null,"abstract":"<div><div>Based on dispersive and hazard rate orders, sharp lower bounds for the maximum order statistic of heterogeneous dependent exponential random variables whose joint distribution is modeled via an Archimedean copula are found. Our results extend and refine a recent contribution by Amini-Seresht, Khaledi, and Izadkhah (Statist. Probab. Lett. 215 (2024), 110242), by providing tighter bounds under convenient conditions on the generator function of the Archimedean copula.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"227 ","pages":"Article 110514"},"PeriodicalIF":0.7,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144860364","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}