Pub Date : 2026-04-01Epub Date: 2025-12-18DOI: 10.1016/j.spl.2025.110627
Pier Giovanni Bissiri, Matteo Borrotti
Generative models for classification are a well-established method in statistics and machine learning. Martingales posteriors provide a computationally feasible method for performing prior-free Bayesian analysis. This paper aims to address the problem of uncertainty quantification through martingale posteriors for generative models for classification. To this aim, a conditionally identically distributed sequence of observations is considered. An empirical analysis is given.
{"title":"Martingale posteriors for generative classifiers","authors":"Pier Giovanni Bissiri, Matteo Borrotti","doi":"10.1016/j.spl.2025.110627","DOIUrl":"10.1016/j.spl.2025.110627","url":null,"abstract":"<div><div>Generative models for classification are a well-established method in statistics and machine learning. Martingales posteriors provide a computationally feasible method for performing prior-free Bayesian analysis. This paper aims to address the problem of uncertainty quantification through martingale posteriors for generative models for classification. To this aim, a conditionally identically distributed sequence of observations is considered. An empirical analysis is given.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"231 ","pages":"Article 110627"},"PeriodicalIF":0.7,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145792040","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}
Pub Date : 2026-04-01Epub Date: 2025-12-17DOI: 10.1016/j.spl.2025.110624
Sayantan Maitra , Aritra Mandal
The framework of Lie algebra has recently been proposed for establishing duals of various Markov processes. We apply this technique to obtain the dual processes of the Feller diffusion and the infinite dimensional interacting Wright-Fisher diffusion.
{"title":"Lie algebraic duality for some Markov processes","authors":"Sayantan Maitra , Aritra Mandal","doi":"10.1016/j.spl.2025.110624","DOIUrl":"10.1016/j.spl.2025.110624","url":null,"abstract":"<div><div>The framework of Lie algebra has recently been proposed for establishing duals of various Markov processes. We apply this technique to obtain the dual processes of the Feller diffusion and the infinite dimensional interacting Wright-Fisher diffusion.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"231 ","pages":"Article 110624"},"PeriodicalIF":0.7,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145792039","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}
Pub Date : 2026-04-01Epub Date: 2025-12-29DOI: 10.1016/j.spl.2025.110626
Tomasz Rychlik , Magdalena Szymkowiak
Due to Hosking (1990) (J. R. Stat. Soc. Ser. B Stat. Methodol.52, 105–124) all the values of scaled -moments belong to the interval . We prove that 1 is actually the sharp upper bound for every scaled -moment, and is the optimal lower bound for the odd scaled -moments. We present a method of determining the optimal lower bounds on even scaled -moments, which are located in . We also present sharp lower and upper bounds on the -moments based on nonnegative samples and measured in the units being the expectations of the parent distributions.
{"title":"Extreme values of scaled L-moments","authors":"Tomasz Rychlik , Magdalena Szymkowiak","doi":"10.1016/j.spl.2025.110626","DOIUrl":"10.1016/j.spl.2025.110626","url":null,"abstract":"<div><div>Due to Hosking (1990) (<em>J. R. Stat. Soc. Ser. B Stat. Methodol.</em> <strong>52</strong>, 105–124) all the values of scaled <span><math><mi>L</mi></math></span>-moments belong to the interval <span><math><mrow><mo>(</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></math></span>. We prove that 1 is actually the sharp upper bound for every scaled <span><math><mi>L</mi></math></span>-moment, and <span><math><mrow><mo>−</mo><mn>1</mn></mrow></math></span> is the optimal lower bound for the odd scaled <span><math><mi>L</mi></math></span>-moments. We present a method of determining the optimal lower bounds on even scaled <span><math><mi>L</mi></math></span>-moments, which are located in <span><math><mrow><mo>(</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow></math></span>. We also present sharp lower and upper bounds on the <span><math><mi>L</mi></math></span>-moments based on nonnegative samples and measured in the units being the expectations of the parent distributions.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"231 ","pages":"Article 110626"},"PeriodicalIF":0.7,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145884650","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}
Pub Date : 2026-04-01Epub Date: 2025-11-11DOI: 10.1016/j.spl.2025.110589
Catia Scricciolo
We study the problem of deconvolving an unknown distribution function when the error distribution is ordinary smooth and unknown. Using data from an auxiliary experiment that provides information about the error distribution, we establish minimax-optimal convergence rates (up to logarithmic factors) with respect to the 1-Wasserstein metric for a kernel-based distribution function estimator over the full range of Hölder-type classes of densities on . Furthermore, we propose a rate-adaptive, data-driven estimation procedure that automatically selects the optimal bandwidth across -Hölder-type classes of mixing densities for , requiring no prior knowledge of the regularity parameters.
{"title":"Adaptive minimax-optimal Wasserstein deconvolution with unknown error distributions","authors":"Catia Scricciolo","doi":"10.1016/j.spl.2025.110589","DOIUrl":"10.1016/j.spl.2025.110589","url":null,"abstract":"<div><div>We study the problem of deconvolving an unknown distribution function when the error distribution is ordinary smooth and unknown. Using data from an auxiliary experiment that provides information about the error distribution, we establish minimax-optimal convergence rates (up to logarithmic factors) with respect to the 1-Wasserstein metric for a kernel-based distribution function estimator over the full range of Hölder-type classes of densities on <span><math><mi>R</mi></math></span>. Furthermore, we propose a rate-adaptive, data-driven estimation procedure that automatically selects the optimal bandwidth across <span><math><mi>α</mi></math></span>-Hölder-type classes of mixing densities for <span><math><mrow><mi>α</mi><mo>≥</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></math></span>, requiring no prior knowledge of the regularity parameters.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"230 ","pages":"Article 110589"},"PeriodicalIF":0.7,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145529166","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}
Pub Date : 2026-04-01Epub Date: 2025-11-24DOI: 10.1016/j.spl.2025.110608
Cinzia Di Nuzzo, Salvatore Ingrassia, Luca Scaffidi Domianello
Directional distributions requires the evaluation of complicated normalizing constants, even for the univariate von Mises. For this reason, maximum likelihood estimation methods are often difficult to apply in practice. To address this issue, we present an approach based on Noise Contrastive Estimation (NCE), a statistical learning technique used for parameter estimation in non-normalized statistical models. In NCE, the estimation problem is reformulated as a binary classification task. In this paper, we focus on fitting mixtures of von Mises distributions, with particular emphasis on toroidal data. Our application to real data, in which we compare several estimation methods, suggests that NCE is a promising alternative for parameter inference in finite mixtures of directional distributions.
{"title":"Fitting mixtures of von Mises distributions via noise contrastive estimation","authors":"Cinzia Di Nuzzo, Salvatore Ingrassia, Luca Scaffidi Domianello","doi":"10.1016/j.spl.2025.110608","DOIUrl":"10.1016/j.spl.2025.110608","url":null,"abstract":"<div><div>Directional distributions requires the evaluation of complicated normalizing constants, even for the univariate von Mises. For this reason, maximum likelihood estimation methods are often difficult to apply in practice. To address this issue, we present an approach based on Noise Contrastive Estimation (NCE), a statistical learning technique used for parameter estimation in non-normalized statistical models. In NCE, the estimation problem is reformulated as a binary classification task. In this paper, we focus on fitting mixtures of von Mises distributions, with particular emphasis on toroidal data. Our application to real data, in which we compare several estimation methods, suggests that NCE is a promising alternative for parameter inference in finite mixtures of directional distributions.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"230 ","pages":"Article 110608"},"PeriodicalIF":0.7,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145624241","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}
Pub Date : 2026-04-01Epub Date: 2025-11-20DOI: 10.1016/j.spl.2025.110606
Luis A. Arteaga-Molina, Juan M. Rodriguez-Poo
This paper proposes a Generalized Likelihood Ratio test for assessing coefficient constancy in varying coefficient models with endogenous regressors. The test accommodates endogeneity through a nonparametric instrumental variables framework and is explicitly designed for time series data, allowing for serial dependence via mixing conditions.
{"title":"A Generalized Likelihood Ratio test for constancy in varying coefficient models with endogenous regressors","authors":"Luis A. Arteaga-Molina, Juan M. Rodriguez-Poo","doi":"10.1016/j.spl.2025.110606","DOIUrl":"10.1016/j.spl.2025.110606","url":null,"abstract":"<div><div>This paper proposes a Generalized Likelihood Ratio test for assessing coefficient constancy in varying coefficient models with endogenous regressors. The test accommodates endogeneity through a nonparametric instrumental variables framework and is explicitly designed for time series data, allowing for serial dependence via mixing conditions.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"230 ","pages":"Article 110606"},"PeriodicalIF":0.7,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145580284","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}
Pub Date : 2026-04-01Epub Date: 2025-11-25DOI: 10.1016/j.spl.2025.110612
Lê Vǎn Thành
Gut (2004) provided necessary and sufficient conditions for the weak law of large numbers with regularly varying norming sequences. This paper shows that Gut’s conditions are also necessary and sufficient for a mean convergence result for the maximum of the weighted sums. A complement to the main result in Boukhari (2022) is also presented. The sharpness of the main theorems is illustrated by three examples.
{"title":"Mean convergence for the maximum of weighted sums of negatively associated random variables under Gut’s condition","authors":"Lê Vǎn Thành","doi":"10.1016/j.spl.2025.110612","DOIUrl":"10.1016/j.spl.2025.110612","url":null,"abstract":"<div><div>Gut (2004) provided necessary and sufficient conditions for the weak law of large numbers with regularly varying norming sequences. This paper shows that Gut’s conditions are also necessary and sufficient for a mean convergence result for the maximum of the weighted sums. A complement to the main result in Boukhari (2022) is also presented. The sharpness of the main theorems is illustrated by three examples.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"230 ","pages":"Article 110612"},"PeriodicalIF":0.7,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145693577","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}
Pub Date : 2026-04-01Epub Date: 2025-11-24DOI: 10.1016/j.spl.2025.110610
M. Dhillon, K.K. Kataria
In this paper, we introduce the elephant random walk (ERW) with memory consisting of randomly selected steps from its history. It is a time-changed variant of the standard elephant random walk with memory consisting of its full history. At each time point, the time changing component is the composition of two uniformly distributed independent random variables with support over all the past steps. Several conditional distributional properties including the conditional mean increments and conditional displacement of ERW with random memory are obtained. Using these conditional results, we derive the recursive and explicit expressions for the mean increments and mean displacement of the walk.
{"title":"On elephant random walk with random memory","authors":"M. Dhillon, K.K. Kataria","doi":"10.1016/j.spl.2025.110610","DOIUrl":"10.1016/j.spl.2025.110610","url":null,"abstract":"<div><div>In this paper, we introduce the elephant random walk (ERW) with memory consisting of randomly selected steps from its history. It is a time-changed variant of the standard elephant random walk with memory consisting of its full history. At each time point, the time changing component is the composition of two uniformly distributed independent random variables with support over all the past steps. Several conditional distributional properties including the conditional mean increments and conditional displacement of ERW with random memory are obtained. Using these conditional results, we derive the recursive and explicit expressions for the mean increments and mean displacement of the walk.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"230 ","pages":"Article 110610"},"PeriodicalIF":0.7,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145624243","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}
Pub Date : 2026-04-01Epub Date: 2025-11-17DOI: 10.1016/j.spl.2025.110602
Doudou Li , Han Liu , Mei Zhang
In this paper, we consider a subcritical Galton–Watson branching process with state-dependent immigration , where immigration is allowed to enter iff the previous generation was empty. Under the exponential moment conditions of branching and immigration, we obtain the large deviations rate of the total population of up to time .
{"title":"Large deviations for a subcritical Galton–Watson process with state-dependent immigration","authors":"Doudou Li , Han Liu , Mei Zhang","doi":"10.1016/j.spl.2025.110602","DOIUrl":"10.1016/j.spl.2025.110602","url":null,"abstract":"<div><div>In this paper, we consider a subcritical Galton–Watson branching process with state-dependent immigration <span><math><mi>X</mi></math></span>, where immigration is allowed to enter iff the previous generation was empty. Under the exponential moment conditions of branching and immigration, we obtain the large deviations rate of the total population of <span><math><mi>X</mi></math></span> up to time <span><math><mi>n</mi></math></span>.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"230 ","pages":"Article 110602"},"PeriodicalIF":0.7,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145624244","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}
Pub Date : 2026-04-01Epub Date: 2025-11-22DOI: 10.1016/j.spl.2025.110605
T.E. Govindan
The paper studies semilinear stochastic evolution equations in a real Hilbert space. The main goal is to consider the Trotter-Kato approximations of mild solutions of such equations using local Lipschitz conditions on the nonlinear terms. The results obtained are new and generalize some of the results from Govindan (2015).
{"title":"Trotter-Kato approximations of stochastic evolution equations with local Lipschitz nonlinearities","authors":"T.E. Govindan","doi":"10.1016/j.spl.2025.110605","DOIUrl":"10.1016/j.spl.2025.110605","url":null,"abstract":"<div><div>The paper studies semilinear stochastic evolution equations in a real Hilbert space. The main goal is to consider the Trotter-Kato approximations of mild solutions of such equations using local Lipschitz conditions on the nonlinear terms. The results obtained are new and generalize some of the results from <span><span>Govindan (2015)</span></span>.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"230 ","pages":"Article 110605"},"PeriodicalIF":0.7,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145624245","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}
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