Pub Date : 2025-12-14DOI: 10.1016/j.spl.2025.110623
Weiwei Zhuang, Yuting Su, Taizhong Hu
Negative dependence emerges through conditioning. In this paper, we establish sufficient conditions for a random vector to exhibit negative regression dependence, negative left-tail dependence and/or negative right-tail dependence when conditioned on the event that its component sum equals a constant or falls within a specified interval. Counterexamples are presented to delineate the conceptual distinctions among some notions of negative dependence.
{"title":"Generating negative regression dependence via conditioning operations","authors":"Weiwei Zhuang, Yuting Su, Taizhong Hu","doi":"10.1016/j.spl.2025.110623","DOIUrl":"10.1016/j.spl.2025.110623","url":null,"abstract":"<div><div>Negative dependence emerges through conditioning. In this paper, we establish sufficient conditions for a random vector to exhibit negative regression dependence, negative left-tail dependence and/or negative right-tail dependence when conditioned on the event that its component sum equals a constant or falls within a specified interval. Counterexamples are presented to delineate the conceptual distinctions among some notions of negative dependence.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"231 ","pages":"Article 110623"},"PeriodicalIF":0.7,"publicationDate":"2025-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145792042","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 : 2025-12-11DOI: 10.1016/j.spl.2025.110621
Lisa Parveen
Various properties of the ordering notion, namely decreasing in mean time to failure (DMTTF) order has been explored. Connections between DMTTF order and other well-known partial orderings of life distributions are established. Interrelationships with certain variability orderings are also explored. The applicability of the results has been demonstrated in the context of coherent systems with dependent but identically distributed components.
{"title":"On some properties of a partial ordering based on the mean time to failure function","authors":"Lisa Parveen","doi":"10.1016/j.spl.2025.110621","DOIUrl":"10.1016/j.spl.2025.110621","url":null,"abstract":"<div><div>Various properties of the ordering notion, namely decreasing in mean time to failure (DMTTF) order has been explored. Connections between DMTTF order and other well-known partial orderings of life distributions are established. Interrelationships with certain variability orderings are also explored. The applicability of the results has been demonstrated in the context of coherent systems with dependent but identically distributed components.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"231 ","pages":"Article 110621"},"PeriodicalIF":0.7,"publicationDate":"2025-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145786940","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 : 2025-12-06DOI: 10.1016/j.spl.2025.110619
Xuekang Zhang, Sijia Qiao
In this paper, we study the parameter estimation for non-stationary -stable Ornstein–Uhlenbeck processes with constant drift based on continuous observations. The consistency and limiting distributions for the estimators are obtained by integration by parts, the strong law of large numbers and the inner clock property for the -stable stochastic integral.
{"title":"Parameter estimation for non-stationary α-stable Ornstein–Uhlenbeck processes with constant drift","authors":"Xuekang Zhang, Sijia Qiao","doi":"10.1016/j.spl.2025.110619","DOIUrl":"10.1016/j.spl.2025.110619","url":null,"abstract":"<div><div>In this paper, we study the parameter estimation for non-stationary <span><math><mi>α</mi></math></span>-stable Ornstein–Uhlenbeck processes with constant drift based on continuous observations. The consistency and limiting distributions for the estimators are obtained by integration by parts, the strong law of large numbers and the inner clock property for the <span><math><mi>α</mi></math></span>-stable stochastic integral.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"231 ","pages":"Article 110619"},"PeriodicalIF":0.7,"publicationDate":"2025-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145738797","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 : 2025-12-06DOI: 10.1016/j.spl.2025.110620
Yanhui Jiao , Yanpeng Li
This note establishes the log-convexity of the sequence of th moments of averages of i.i.d. Gamma random variables for by using the properties of the Gamma function. Moreover, for integral , the log-convexity for the sequence of Poisson distribution is also demonstrated.
{"title":"Log-convexity of moments of averages of i.i.d. Gamma and Poisson random variables","authors":"Yanhui Jiao , Yanpeng Li","doi":"10.1016/j.spl.2025.110620","DOIUrl":"10.1016/j.spl.2025.110620","url":null,"abstract":"<div><div>This note establishes the log-convexity of the sequence of <span><math><mi>p</mi></math></span>th moments of averages of i.i.d. Gamma random variables for <span><math><mrow><mi>p</mi><mo>≥</mo><mn>1</mn></mrow></math></span> by using the properties of the Gamma function. Moreover, for integral <span><math><mrow><mi>p</mi><mo>≥</mo><mn>1</mn></mrow></math></span>, the log-convexity for the sequence of Poisson distribution is also demonstrated.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"231 ","pages":"Article 110620"},"PeriodicalIF":0.7,"publicationDate":"2025-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145705792","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 : 2025-11-27DOI: 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}
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