Pub Date : 2025-09-22DOI: 10.1016/j.spl.2025.110556
Dimitrios Katselis , Boris I. Godoy , Rodrigo Carvajal , Juan C. Agüero
The filter for a finite HMM at time is expressed in terms of a stochastic matrix . We relate arbitrary pairs of rows in with the corresponding pairs of rows in the underlying -step transition matrix .
{"title":"A note on the structure of the filtering recursion for finite HMMs","authors":"Dimitrios Katselis , Boris I. Godoy , Rodrigo Carvajal , 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":"2025-09-22","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}
Pub Date : 2025-09-22DOI: 10.1016/j.spl.2025.110555
Mathias Barreto , Olivier Marchal , Julyan Arbel
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.
{"title":"Optimal sub-Gaussian variance proxy for truncated Gaussian and exponential random variables","authors":"Mathias Barreto , Olivier Marchal , 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":"2025-09-22","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}
Pub Date : 2025-09-20DOI: 10.1016/j.spl.2025.110559
Neil Dey, Ryan Martin, Jonathan P. Williams
Compared to p-values, e-values provably guarantee safe, valid inference. Applications often require consideration of multiple hypotheses simultaneously, and tools for handling such cases using e-values can be found in the relevant literature. Standard e-value constructions, however, require distributional assumptions that may not be justifiable. This short paper demonstrates that, depending on the multiple testing context, the generalized universal inference framework is well-suited for use with the existing e-value merging and adjustment strategies to control frequentist error rates in multiple testing when the quantities of interest are minimizers of risk functions, thereby avoiding the need for certain distributional assumptions. We demonstrate the strong performance of this general approach in a simulation study involving significance testing in quantile regression.
{"title":"Multiple testing in generalized universal inference","authors":"Neil Dey, Ryan Martin, Jonathan P. Williams","doi":"10.1016/j.spl.2025.110559","DOIUrl":"10.1016/j.spl.2025.110559","url":null,"abstract":"<div><div>Compared to p-values, e-values provably guarantee safe, valid inference. Applications often require consideration of multiple hypotheses simultaneously, and tools for handling such cases using e-values can be found in the relevant literature. Standard e-value constructions, however, require distributional assumptions that may not be justifiable. This short paper demonstrates that, depending on the multiple testing context, the generalized universal inference framework is well-suited for use with the existing e-value merging and adjustment strategies to control frequentist error rates in multiple testing when the quantities of interest are minimizers of risk functions, thereby avoiding the need for certain distributional assumptions. We demonstrate the strong performance of this general approach in a simulation study involving significance testing in quantile regression.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"228 ","pages":"Article 110559"},"PeriodicalIF":0.7,"publicationDate":"2025-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222579","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 : 2025-09-17DOI: 10.1016/j.spl.2025.110557
Hang Zou , Yunlu Jiang
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.
{"title":"Communication-efficient distributed robust variable selection for heterogeneous massive data","authors":"Hang Zou , 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":"2025-09-17","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}
Pub Date : 2025-09-12DOI: 10.1016/j.spl.2025.110554
Robert E. Gaunt
We represent the product of two correlated normal random variables, and more generally the sum of independent copies of such random variables, as a difference of two independent noncentral chi-square random variables (which we refer to as the noncentral chi-square difference distribution). As a consequence, we obtain, amongst other results, an exact formula for the probability density function of the noncentral chi-square difference distribution, a Stein characterisation of the noncentral chi-square difference distribution, a simple formula for the moments of the sum of independent copies of the product of correlated normal random variables, an exact formula for the probability that such a random variable is negative, and also show that such random variables are self-decomposable and provide a Lévy–Khintchine representation of the characteristic function.
{"title":"On the product of correlated normal random variables and the noncentral chi-square difference distribution","authors":"Robert E. Gaunt","doi":"10.1016/j.spl.2025.110554","DOIUrl":"10.1016/j.spl.2025.110554","url":null,"abstract":"<div><div>We represent the product of two correlated normal random variables, and more generally the sum of independent copies of such random variables, as a difference of two independent noncentral chi-square random variables (which we refer to as the noncentral chi-square difference distribution). As a consequence, we obtain, amongst other results, an exact formula for the probability density function of the noncentral chi-square difference distribution, a Stein characterisation of the noncentral chi-square difference distribution, a simple formula for the moments of the sum of independent copies of the product of correlated normal random variables, an exact formula for the probability that such a random variable is negative, and also show that such random variables are self-decomposable and provide a Lévy–Khintchine representation of the characteristic function.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"227 ","pages":"Article 110554"},"PeriodicalIF":0.7,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145046175","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 : 2025-09-11DOI: 10.1016/j.spl.2025.110553
Yiming Jiang , Yujue Wang , Jie Xue
In this paper, we study the stochastic generalized Burgers equation driven by a white-colored noise with the -order heat kernel. First we construct a parametric estimator of the drift parameter through temporal quadratic variation of the solution. Then we obtain the consistency and convergence rate of the estimator.
{"title":"Parameter estimation of Burgers equations driven by white-colored noise","authors":"Yiming Jiang , Yujue Wang , Jie Xue","doi":"10.1016/j.spl.2025.110553","DOIUrl":"10.1016/j.spl.2025.110553","url":null,"abstract":"<div><div>In this paper, we study the stochastic generalized Burgers equation driven by a white-colored noise with the <span><math><mi>α</mi></math></span>-order heat kernel. First we construct a parametric estimator of the drift parameter through temporal quadratic variation of the solution. Then we obtain the consistency and convergence rate of the estimator.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"227 ","pages":"Article 110553"},"PeriodicalIF":0.7,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145046179","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 : 2025-09-11DOI: 10.1016/j.spl.2025.110551
Nguyen Van Quang , Ali Talebi
In this paper, we establish some general laws of large numbers for sequence of measurable operators such that several known strong law of large numbers (LLN) in von Neumann algebras. One of our main achievements extends the main result of Jajte (2003) in some senses such that Batty’s strong LLN and Łuczak’s result are obtained as special cases. The result is new even in the case of classical random variables.
{"title":"Some general strong laws of large numbers for sequence of measurable operators","authors":"Nguyen Van Quang , Ali Talebi","doi":"10.1016/j.spl.2025.110551","DOIUrl":"10.1016/j.spl.2025.110551","url":null,"abstract":"<div><div>In this paper, we establish some general laws of large numbers for sequence of measurable operators such that several known strong law of large numbers (LLN) in von Neumann algebras. One of our main achievements extends the main result of Jajte (2003) in some senses such that Batty’s strong LLN and Łuczak’s result are obtained as special cases. The result is new even in the case of classical random variables.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"227 ","pages":"Article 110551"},"PeriodicalIF":0.7,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145046176","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 : 2025-09-10DOI: 10.1016/j.spl.2025.110550
Ting Zhang , Lulu Tian , Tianyi Qi
For the call function with some fixed , we apply Stein’s method to give the upper bounds of normal approximation under the weaker moment condition, containing both uniform and non uniform situations. Specifically, we discuss a sum of -dependent and identically distributed random variables with weaker ()-th moment for some . Our results enable the application in call function to possess a broader field with normal approximation techniques.
{"title":"Normal approximation for call function of m-dependent random variables with 2+δ-th moment","authors":"Ting Zhang , Lulu Tian , Tianyi Qi","doi":"10.1016/j.spl.2025.110550","DOIUrl":"10.1016/j.spl.2025.110550","url":null,"abstract":"<div><div>For the call function <span><math><mrow><msub><mrow><mi>h</mi></mrow><mrow><mi>k</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mo>max</mo><mrow><mo>{</mo><mi>x</mi><mo>−</mo><mi>k</mi><mo>,</mo><mn>0</mn><mo>}</mo></mrow></mrow></math></span> with some fixed <span><math><mrow><mi>k</mi><mo>></mo><mn>0</mn></mrow></math></span>, we apply Stein’s method to give the upper bounds of normal approximation under the weaker moment condition, containing both uniform and non uniform situations. Specifically, we discuss a sum of <span><math><mi>m</mi></math></span>-dependent and identically distributed random variables with weaker (<span><math><mrow><mn>2</mn><mo>+</mo><mi>δ</mi></mrow></math></span>)-th moment for some <span><math><mrow><mi>δ</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>. Our results enable the application in call function to possess a broader field with normal approximation techniques.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"227 ","pages":"Article 110550"},"PeriodicalIF":0.7,"publicationDate":"2025-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145046178","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 : 2025-09-09DOI: 10.1016/j.spl.2025.110549
Yaqin Sun , Jingqi Han , Litan Yan
By the quasi-likelihood method, in this note we consider parameter estimation of the fractional heat equation with initial condition , where is a space–time white noise and is the fractional Laplacian with . By using the quasi-likelihood method we obtain the estimator of and give the asymptotic behaviors of the estimator provided that the spatial process can be observed at some discrete points with , for some , as .
{"title":"Quasi-likelihood estimation for stochastic fractional heat equation","authors":"Yaqin Sun , Jingqi Han , 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><</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":"2025-09-09","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}
Pub Date : 2025-09-09DOI: 10.1016/j.spl.2025.110548
Tao Wang
In this paper, we present the criteria for super-Poincaré inequalities by using the first Dirichlet eigenvalues under some proper assumptions. Furthermore, I will illustrate the applicability of the result to a range of classic models, including jump processes, diffusion processes, and SDEs driven by symmetric stable processes.
{"title":"Dirichlet eigenvalue criteria for super Poincaré inequalities","authors":"Tao Wang","doi":"10.1016/j.spl.2025.110548","DOIUrl":"10.1016/j.spl.2025.110548","url":null,"abstract":"<div><div>In this paper, we present the criteria for super-Poincaré inequalities by using the first Dirichlet eigenvalues under some proper assumptions. Furthermore, I will illustrate the applicability of the result to a range of classic models, including jump processes, diffusion processes, and SDEs driven by symmetric stable processes.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"227 ","pages":"Article 110548"},"PeriodicalIF":0.7,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145046177","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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