Statistics & Probability Letters最新文献

{"title":"Mixed binomial moments of overlapping r-runs in multicolour Hoppe–Pólya urns","authors":"Djilali Ait Aoudia","doi":"10.1016/j.spl.2026.110664","DOIUrl":"10.1016/j.spl.2026.110664","url":null,"abstract":"<div><div>We consider a multicolour Hoppe–Pólya urn with unit reinforcement and initial composition <span><math><mrow><mo>(</mo><msub><mrow><mi>a</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>,</mo><mi>b</mi><mo>)</mo></mrow></math></span>. For each colour <span><math><mi>j</mi></math></span> and integer <span><math><mrow><mi>r</mi><mo>≥</mo><mn>2</mn></mrow></math></span>, let <span><math><msubsup><mrow><mi>S</mi></mrow><mrow><mi>n</mi><mo>,</mo><mi>j</mi></mrow><mrow><mrow><mo>(</mo><mi>r</mi><mo>)</mo></mrow></mrow></msubsup></math></span> denote the number of consecutive <span><math><mi>r</mi></math></span>-runs of colour <span><math><mi>j</mi></math></span> among the first <span><math><mi>n</mi></math></span> draws. We derive a closed form for the joint mixed factorial (hence binomial) moments of <span><math><mrow><mo>(</mo><msubsup><mrow><mi>S</mi></mrow><mrow><mi>n</mi><mo>,</mo><mn>1</mn></mrow><mrow><mrow><mo>(</mo><mi>r</mi><mo>)</mo></mrow></mrow></msubsup><mo>,</mo><mo>…</mo><mo>,</mo><msubsup><mrow><mi>S</mi></mrow><mrow><mi>n</mi><mo>,</mo><mi>m</mi></mrow><mrow><mrow><mo>(</mo><mi>r</mi><mo>)</mo></mrow></mrow></msubsup><mo>)</mo></mrow></math></span> in compact Pochhammer form. As a consequence, <span><span><span><math><mrow><msup><mrow><mi>n</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mrow><mo>(</mo><msubsup><mrow><mi>S</mi></mrow><mrow><mi>n</mi><mo>,</mo><mn>1</mn></mrow><mrow><mrow><mo>(</mo><mi>r</mi><mo>)</mo></mrow></mrow></msubsup><mo>,</mo><mo>…</mo><mo>,</mo><msubsup><mrow><mi>S</mi></mrow><mrow><mi>n</mi><mo>,</mo><mi>m</mi></mrow><mrow><mrow><mo>(</mo><mi>r</mi><mo>)</mo></mrow></mrow></msubsup><mo>)</mo></mrow><mspace></mspace><munderover><mrow><mo>⟶</mo></mrow><mrow><mi>n</mi><mo>→</mo><mi>∞</mi></mrow><mrow><mspace></mspace><mi>L</mi></mrow></munderover><mspace></mspace><mrow><mo>(</mo><msubsup><mrow><mi>U</mi></mrow><mrow><mn>1</mn></mrow><mrow><mi>r</mi></mrow></msubsup><mo>,</mo><mo>…</mo><mo>,</mo><msubsup><mrow><mi>U</mi></mrow><mrow><mi>m</mi></mrow><mrow><mi>r</mi></mrow></msubsup><mo>)</mo></mrow><mo>,</mo><mspace></mspace><mrow><mo>(</mo><msub><mrow><mi>U</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>U</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>)</mo></mrow><mo>∼</mo><mi>Dirichlet</mi><mrow><mo>(</mo><msub><mrow><mi>a</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>,</mo><mi>b</mi><mo>)</mo></mrow><mo>.</mo></mrow></math></span></span></span>Finally, under disjoint Poissonisation, the total number of <span><math><mi>r</mi></math></span>–runs admits an exact Dirichlet–Poisson mixture law.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"233 ","pages":"Article 110664"},"PeriodicalIF":0.7,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146191118","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":"Functional limit theorems for random Lebesgue–Stieltjes convolutions","authors":"Alexander Iksanov ,&nbsp;Wissem Jedidi","doi":"10.1016/j.spl.2026.110684","DOIUrl":"10.1016/j.spl.2026.110684","url":null,"abstract":"<div><div>We prove joint functional limit theorems in the Skorokhod space equipped with the <span><math><msub><mrow><mi>J</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>-topology for successive Lebesgue–Stieltjes convolutions of nondecreasing stochastic processes with themselves. These convolutions arise naturally in coupled branching random walks, where the displacements of individuals relative to their mother’s position are given by the underlying point process rather than its copy. Surprisingly, the numbers of individuals in the <span><math><mi>j</mi></math></span>th generation, with positions less than or equal to <span><math><mi>t</mi></math></span>, exhibit remarkably similar distributional behavior in both standard branching random walks and coupled branching random walks as <span><math><mi>t</mi></math></span> tends to infinity.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"233 ","pages":"Article 110684"},"PeriodicalIF":0.7,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146191120","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":"General M-estimators of location on Riemannian manifolds: Existence and uniqueness","authors":"Jongmin Lee ,&nbsp;Sungkyu Jung","doi":"10.1016/j.spl.2026.110670","DOIUrl":"10.1016/j.spl.2026.110670","url":null,"abstract":"<div><div>We study general M-estimators of location on Riemannian manifolds, extending classical notions such as the Fréchet mean by replacing the squared loss with a broad class of loss functions. Under minimal regularity conditions on the loss function and the underlying probability distribution, we establish theoretical guarantees for the existence and uniqueness of the associated population M-functional and the corresponding sample M-estimators. In particular, we provide sufficient conditions under which the population minimizer set is nonempty and reduces to a singleton, and under which the corresponding sample M-estimator is likewise uniquely defined. Our results offer a general framework for robust location estimation in non-Euclidean geometric spaces and unify prior uniqueness results under a broad class of convex losses.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"233 ","pages":"Article 110670"},"PeriodicalIF":0.7,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146190567","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":"Directional replicability: When can the factor of two be omitted","authors":"Vera Djordjilović ,&nbsp;Tamar Sofer ,&nbsp;Jonathan M. Dreyfuss","doi":"10.1016/j.spl.2026.110662","DOIUrl":"10.1016/j.spl.2026.110662","url":null,"abstract":"<div><div>Directional replicability addresses the question of whether an effect studied across <span><math><mi>n</mi></math></span> independent studies is present with the same direction in at least <span><math><mi>r</mi></math></span> of them, for <span><math><mrow><mi>r</mi><mo>≥</mo><mn>2</mn></mrow></math></span>. When the expected direction of the effect is not specified in advance, the state of the art recommends assessing replicability separately by combining one-sided <span><math><mi>p</mi></math></span>-values for both directions (left and right), and then doubling the smaller of the two resulting combined <span><math><mi>p</mi></math></span>-values to account for multiple testing. In this work, we show that this multiplicative correction is not always necessary, and give a sufficient and necessary condition under which it can be safely omitted.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"233 ","pages":"Article 110662"},"PeriodicalIF":0.7,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146191123","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 caveat on metrizing convergence in distribution on Hilbert spaces","authors":"Federico Bassetti ,&nbsp;Solesne Bourguin ,&nbsp;Simon Campese ,&nbsp;Giovanni Peccati","doi":"10.1016/j.spl.2026.110671","DOIUrl":"10.1016/j.spl.2026.110671","url":null,"abstract":"<div><div>We consider Sobolev-type distances on probability measures over separable Hilbert spaces involving the Schatten-<span><math><mi>p</mi></math></span> norms, which include as special cases a distance first introduced by Bourguin and Campese (2020) when <span><math><mrow><mi>p</mi><mo>=</mo><mn>2</mn></mrow></math></span>, and a distance introduced by Giné and Leon (1980) when <span><math><mrow><mi>p</mi><mo>=</mo><mi>∞</mi></mrow></math></span>. Our analysis shows that, unless <span><math><mrow><mi>p</mi><mo>=</mo><mi>∞</mi></mrow></math></span>, these distances fail to metrize convergence in distribution in infinite dimensions. This clarifies several inconsistencies and misconceptions in the recent literature that arose from confusion between different types of distances.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"233 ","pages":"Article 110671"},"PeriodicalIF":0.7,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146191125","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":"On the robustness of maximum likelihood estimators for the Poisson INAR(1) model","authors":"Subhankar Chattopadhyay ,&nbsp;Sancharee Basak ,&nbsp;Atanu Biswas","doi":"10.1016/j.spl.2026.110659","DOIUrl":"10.1016/j.spl.2026.110659","url":null,"abstract":"<div><div>This article examines the robustness of maximum likelihood estimators in Poisson integer-valued autoregressive processes of order one, which model count time series with autocorrelation and Poisson-distributed innovations. While maximum likelihood estimation is widely used to estimate the autocorrelation parameter <span><math><mi>α</mi></math></span> and the mean parameter <span><math><mi>λ</mi></math></span>, its sensitivity to outliers and model deviations remains insufficiently understood. We use influence function theory to quantify the local impact of infinitesimal contamination on the estimators and compute gross error sensitivity to assess worst-case sensitivity. The methodology connects robust statistical ideas with count time series modeling by providing explicit score expressions and estimating Fisher information by simulation under stationarity. Visual diagnostics, including heatmaps, three-dimensional sensitivity surfaces, and summary tables, identify parameter regimes where the estimators become vulnerable to contamination. The study provides practical guidance and diagnostics for applied researchers in the social sciences and epidemiology.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"233 ","pages":"Article 110659"},"PeriodicalIF":0.7,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146039474","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":"Two-type continuous-state branching processes in varying environments","authors":"Zenghu Li,&nbsp;Junyan Zhang","doi":"10.1016/j.spl.2026.110669","DOIUrl":"10.1016/j.spl.2026.110669","url":null,"abstract":"<div><div>A basic class of two-type continuous-state branching processes in varying environments are constructed by solving the backward equation determining the cumulant semigroup. The parameters of the process are allowed to be càdlàg in time and the difficulty brought about by the bottlenecks are overcome by introducing a suitable moment condition.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"233 ","pages":"Article 110669"},"PeriodicalIF":0.7,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146191124","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":"Turnpike properties for stochastic linear–quadratic optimal control problems with partial observation","authors":"Ruizhe Hu ,&nbsp;Huojun Wu","doi":"10.1016/j.spl.2026.110660","DOIUrl":"10.1016/j.spl.2026.110660","url":null,"abstract":"<div><div>This paper establishes the strong exponential turnpike property for a partially observed stochastic linear–quadratic optimal control problem. We apply an orthogonal decomposition method to decouple the system into filtering and difference processes. Under standard stabilizability and detectability conditions, the convergence of the difference process is proven, leading to the exponential turnpike property with explicitly characterized decay rates. These rates are shown to be governed by the convergence rate between the two decoupled processes.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"233 ","pages":"Article 110660"},"PeriodicalIF":0.7,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146080732","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":"On the distance between mean and geometric median in high dimensions","authors":"Richard Schwank ,&nbsp;Mathias Drton","doi":"10.1016/j.spl.2026.110679","DOIUrl":"10.1016/j.spl.2026.110679","url":null,"abstract":"<div><div>The geometric median, a notion of “center” for multivariate distributions, has gained recent attention in robust statistics and machine learning. Although conceptually distinct from the mean (i.e., expectation), we demonstrate that both are very close in high dimensions when the dependence between the distribution components is suitably controlled. Concretely, we find an upper bound on the distance that vanishes with the dimension asymptotically, and derive a rate-matching first order expansion of the geometric median components. Simulations illustrate and confirm our results.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"233 ","pages":"Article 110679"},"PeriodicalIF":0.7,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146191116","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":"Dynkin games under progressive enlargement of filtration with random time","authors":"Badr Elmansouri ,&nbsp;Mohamed Marzougue ,&nbsp;Mohamed El Jamali","doi":"10.1016/j.spl.2026.110686","DOIUrl":"10.1016/j.spl.2026.110686","url":null,"abstract":"<div><div>This paper characterizes and establishes an explicit relationship between the value processes of a class of Dynkin games under the progressive enlargement <span><math><mi>G</mi></math></span> of a reference filtration <span><math><mi>F</mi></math></span> by a random time <span><math><mi>τ</mi></math></span>, which is not necessarily an <span><math><mi>F</mi></math></span>-stopping time. We prove that solving the valuation problem in <span><math><mi>G</mi></math></span> reduces to solving an associated pricing problem in <span><math><mi>F</mi></math></span>.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"233 ","pages":"Article 110686"},"PeriodicalIF":0.7,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146190564","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}