Pub Date : 2025-11-27DOI: 10.1016/j.spl.2025.110604
Farouk Mselmi
The concept of duality in natural exponential families, as introduced by Letac (2022), establishes a connection to the theory of large deviations. In this paper, we derive the Laplace transform, the link function, and the variance function of dual measures in certain real mixture models. We present examples ranging from simple cases to more complex ones requiring deeper analysis. Furthermore, we prove the existence and infinite divisibility of dual measures in models with intricate structures, particularly those involving the special Lambert function, and determine their associated link and variance functions. The dual measure does not always exist, and in such cases, we provide examples of real mixture models that lack a dual measure.
{"title":"On the duality for real mixture models","authors":"Farouk Mselmi","doi":"10.1016/j.spl.2025.110604","DOIUrl":"10.1016/j.spl.2025.110604","url":null,"abstract":"<div><div>The concept of duality in natural exponential families, as introduced by Letac (2022), establishes a connection to the theory of large deviations. In this paper, we derive the Laplace transform, the link function, and the variance function of dual measures in certain real mixture models. We present examples ranging from simple cases to more complex ones requiring deeper analysis. Furthermore, we prove the existence and infinite divisibility of dual measures in models with intricate structures, particularly those involving the special Lambert function, and determine their associated link and variance functions. The dual measure does not always exist, and in such cases, we provide examples of real mixture models that lack a dual measure.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"230 ","pages":"Article 110604"},"PeriodicalIF":0.7,"publicationDate":"2025-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145624240","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 : 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":"2025-11-25","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 : 2025-11-25DOI: 10.1016/j.spl.2025.110611
Quirin Vogel
We prove a large deviation principle for deep neural networks with Gaussian weights and at most linearly growing activation functions, such as ReLU. This generalizes earlier work, in which bounded and continuous activation functions were considered. In practice, linearly growing activation functions such as ReLU are most commonly used. We furthermore simplify previous expressions for the rate function and provide a power-series expansions for the ReLU case.
{"title":"Large deviations of Gaussian neural networks with ReLU activation","authors":"Quirin Vogel","doi":"10.1016/j.spl.2025.110611","DOIUrl":"10.1016/j.spl.2025.110611","url":null,"abstract":"<div><div>We prove a large deviation principle for deep neural networks with Gaussian weights and at most linearly growing activation functions, such as ReLU. This generalizes earlier work, in which bounded and continuous activation functions were considered. In practice, linearly growing activation functions such as ReLU are most commonly used. We furthermore simplify previous expressions for the rate function and provide a power-series expansions for the ReLU case.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"230 ","pages":"Article 110611"},"PeriodicalIF":0.7,"publicationDate":"2025-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145624248","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 : 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":"2025-11-24","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 : 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":"2025-11-24","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 : 2025-11-22DOI: 10.1016/j.spl.2025.110609
Swarnadeep Datta , Monitirtha Dey
We propose a simple single-step multiple testing procedure that asymptotically controls the family-wise error rate (FWER) at the desired level exactly under the equicorrelated multivariate Gaussian setup. The method is shown to be asymptotically exact using an explicit plug-in estimator for the equicorrelation, and does not require stepwise adjustments. We establish its theoretical properties, including the convergence to the desired error level (along with an estimate of the rate of convergence), and demonstrate its effectiveness through simulation results. We also spell out related extensions to unknown equicorrelation, block-correlated structures and generalized FWER control.
{"title":"An asymptotically exact multiple testing procedure under dependence","authors":"Swarnadeep Datta , Monitirtha Dey","doi":"10.1016/j.spl.2025.110609","DOIUrl":"10.1016/j.spl.2025.110609","url":null,"abstract":"<div><div>We propose a simple single-step multiple testing procedure that asymptotically controls the family-wise error rate (FWER) at the desired level exactly under the equicorrelated multivariate Gaussian setup. The method is shown to be asymptotically exact using an explicit plug-in estimator for the equicorrelation, and does not require stepwise adjustments. We establish its theoretical properties, including the convergence to the desired error level (along with an estimate of the rate of convergence), and demonstrate its effectiveness through simulation results. We also spell out related extensions to unknown equicorrelation, block-correlated structures and generalized FWER control.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"230 ","pages":"Article 110609"},"PeriodicalIF":0.7,"publicationDate":"2025-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145624246","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 : 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":"2025-11-22","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}
Pub Date : 2025-11-21DOI: 10.1016/j.spl.2025.110607
Danijel Krizmanić
For a stationary sequence of random variables we derive a self-normalized functional limit theorem under joint regular variation with index and weak dependence conditions. The convergence takes place in the space of real-valued càdlàg functions on with the Skorokhod topology.
{"title":"A functional limit theorem for self-normalized partial sum processes in the M1 topology","authors":"Danijel Krizmanić","doi":"10.1016/j.spl.2025.110607","DOIUrl":"10.1016/j.spl.2025.110607","url":null,"abstract":"<div><div>For a stationary sequence of random variables we derive a self-normalized functional limit theorem under joint regular variation with index <span><math><mrow><mi>α</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></mrow></math></span> and weak dependence conditions. The convergence takes place in the space of real-valued càdlàg functions on <span><math><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></math></span> with the Skorokhod <span><math><msub><mrow><mi>M</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> topology.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"230 ","pages":"Article 110607"},"PeriodicalIF":0.7,"publicationDate":"2025-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145624242","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 : 2025-11-21DOI: 10.1016/j.spl.2025.110591
Tianyi Wang, Guanghui Wang, Zhaojun Wang, Changliang Zou
Permutation-based partial-correlation tests guarantee finite-sample Type I error control under any fixed design and exchangeable noise, yet their power can collapse when the permutation-augmented design aligns too closely with the covariate of interest. We remedy this by fixing a design-driven subset of rows and permuting only the remainder. The fixed rows are chosen by a greedy algorithm that maximizes a lower bound on power. This strategy reduces covariate-permutation collinearity while preserving worst-case Type I error control. Simulations confirm that this refinement maintains nominal size and delivers substantial power gains over original unrestricted permutations, especially in high-collinearity regimes.
{"title":"Power enhancement of permutation-augmented partial-correlation tests via fixed-row permutations","authors":"Tianyi Wang, Guanghui Wang, Zhaojun Wang, Changliang Zou","doi":"10.1016/j.spl.2025.110591","DOIUrl":"10.1016/j.spl.2025.110591","url":null,"abstract":"<div><div>Permutation-based partial-correlation tests guarantee finite-sample Type I error control under any fixed design and exchangeable noise, yet their power can collapse when the permutation-augmented design aligns too closely with the covariate of interest. We remedy this by fixing a design-driven subset of rows and permuting only the remainder. The fixed rows are chosen by a greedy algorithm that maximizes a lower bound on power. This strategy reduces covariate-permutation collinearity while preserving worst-case Type I error control. Simulations confirm that this refinement maintains nominal size and delivers substantial power gains over original unrestricted permutations, especially in high-collinearity regimes.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"230 ","pages":"Article 110591"},"PeriodicalIF":0.7,"publicationDate":"2025-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145624247","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 : 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":"2025-11-20","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}
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