Pub 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":"2025-12-29","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}
In reliability engineering, the -shock model is used to study shock-exposed systems that are sensitive to the length of the time distance between consecutive shocks. When the system failure depends on a certain number of consecutive shocks with an inter-arrival time within a critical range, we are dealing with a run-based -shock model. In this paper, a new run-based -shock model is introduced, under which the system fails when an inter-arrival time is less than a critical threshold for the first time or consecutive inter-arrival times fall in the interval , for . We study the probability behavior of the system’s stopping time as well as the survival of the system under the proposed model. As an illustrative example, we examine the survival of the system when the arrival of shocks follows a Poisson process. Furthermore, an example of applications is provided to illustrate possible application aspects.
{"title":"On a run-based δ-shock model with two critical levels","authors":"Maxim Finkelstein , Hamed Lorvand , Reza Farhadian","doi":"10.1016/j.spl.2025.110632","DOIUrl":"10.1016/j.spl.2025.110632","url":null,"abstract":"<div><div>In reliability engineering, the <span><math><mi>δ</mi></math></span>-shock model is used to study shock-exposed systems that are sensitive to the length of the time distance between consecutive shocks. When the system failure depends on a certain number of consecutive shocks with an inter-arrival time within a critical range, we are dealing with a run-based <span><math><mi>δ</mi></math></span>-shock model. In this paper, a new run-based <span><math><mi>δ</mi></math></span>-shock model is introduced, under which the system fails when an inter-arrival time is less than a critical threshold <span><math><msub><mrow><mi>δ</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> for the first time or <span><math><mi>k</mi></math></span> consecutive inter-arrival times fall in the interval <span><math><mrow><mo>(</mo><msub><mrow><mi>δ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>δ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo></mrow></math></span>, for <span><math><mrow><mn>0</mn><mo>≤</mo><msub><mrow><mi>δ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo><</mo><msub><mrow><mi>δ</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span>. We study the probability behavior of the system’s stopping time as well as the survival of the system under the proposed model. As an illustrative example, we examine the survival of the system when the arrival of shocks follows a Poisson process. Furthermore, an example of applications is provided to illustrate possible application aspects.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"232 ","pages":"Article 110632"},"PeriodicalIF":0.7,"publicationDate":"2025-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145886068","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 : 2025-12-24DOI: 10.1016/j.spl.2025.110630
Phan Tri Kien , Nguyen Van Quang , Nguyen Van Huan
The aim of this paper is to establish weak laws of large numbers together with convergence rates for random sums of -orthogonal fields and adapted fields. Some well-known results are extended to double sums with random indices.
{"title":"Weak laws of large numbers together with convergence rates for random sums of random fields","authors":"Phan Tri Kien , Nguyen Van Quang , Nguyen Van Huan","doi":"10.1016/j.spl.2025.110630","DOIUrl":"10.1016/j.spl.2025.110630","url":null,"abstract":"<div><div>The aim of this paper is to establish weak laws of large numbers together with convergence rates for random sums of <span><math><mi>M</mi></math></span>-orthogonal fields and adapted fields. Some well-known results are extended to double sums with random indices.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"231 ","pages":"Article 110630"},"PeriodicalIF":0.7,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841454","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 : 2025-12-24DOI: 10.1016/j.spl.2025.110631
Yongfeng Wu , Mei Guan
The authors study the complete moment convergence for pairwise independent and identically distributed (i.i.d.) random variables with regularly varying moments. The obtained results in this work extend and improve the corresponding theorems of Stoica and Li (2025) and Chen et al. (2014).
研究了矩有规则变化的两两独立同分布随机变量的矩完全收敛性。本文所得结果扩展并改进了Stoica and Li（2025）和Chen et al.（2014）的相应定理。
{"title":"Complete moment convergence for pairwise i.i.d. random variables with regularly varying moments","authors":"Yongfeng Wu , Mei Guan","doi":"10.1016/j.spl.2025.110631","DOIUrl":"10.1016/j.spl.2025.110631","url":null,"abstract":"<div><div>The authors study the complete moment convergence for pairwise independent and identically distributed (i.i.d.) random variables with regularly varying moments. The obtained results in this work extend and improve the corresponding theorems of Stoica and Li (2025) and Chen et al. (2014).</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"231 ","pages":"Article 110631"},"PeriodicalIF":0.7,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841474","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 : 2025-12-19DOI: 10.1016/j.spl.2025.110629
Badr Elmansouri , Mohamed Marzougue
In this note, we establish the existence of a minimal solution for a class of reflected generalized backward doubly stochastic differential equations with continuous and stochastic linear growth coefficients. The reflecting obstacle is not assumed to be right-continuous, but only right-upper semi-continuous and left-limited, and the noise is driven by two mutually independent Brownian motions and an independent integer-valued random measure. Our analysis begins with the case of stochastic Lipschitz coefficients, where we prove the existence and uniqueness results along with presenting a comparison result, which then allows us to derive the main existence finding of a minimal solution.
{"title":"Generalized reflected backward doubly SDEs with irregular barriers and continuous coefficients","authors":"Badr Elmansouri , Mohamed Marzougue","doi":"10.1016/j.spl.2025.110629","DOIUrl":"10.1016/j.spl.2025.110629","url":null,"abstract":"<div><div>In this note, we establish the existence of a minimal solution for a class of reflected generalized backward doubly stochastic differential equations with continuous and stochastic linear growth coefficients. The reflecting obstacle is not assumed to be right-continuous, but only right-upper semi-continuous and left-limited, and the noise is driven by two mutually independent Brownian motions and an independent integer-valued random measure. Our analysis begins with the case of stochastic Lipschitz coefficients, where we prove the existence and uniqueness results along with presenting a comparison result, which then allows us to derive the main existence finding of a minimal solution.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"231 ","pages":"Article 110629"},"PeriodicalIF":0.7,"publicationDate":"2025-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841455","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 : 2025-12-19DOI: 10.1016/j.spl.2025.110628
Minhan Wen , Ruoning Guan , Hui Jiang
In this paper, we consider the asymptotic properties of the maximum likelihood estimator of the drift coefficient in the Rayleigh diffusion process. Via the parameter-dependent change of measure method and precise asymptotic analysis techniques, we obtain the optimal Cramér-type moderate deviations and uniform Berry–Esseen bound.
{"title":"Berry–Esseen bound and Cramér-type moderate deviations of the maximum likelihood estimator in Rayleigh diffusion process","authors":"Minhan Wen , Ruoning Guan , Hui Jiang","doi":"10.1016/j.spl.2025.110628","DOIUrl":"10.1016/j.spl.2025.110628","url":null,"abstract":"<div><div>In this paper, we consider the asymptotic properties of the maximum likelihood estimator of the drift coefficient in the Rayleigh diffusion process. Via the parameter-dependent change of measure method and precise asymptotic analysis techniques, we obtain the optimal Cramér-type moderate deviations and uniform Berry–Esseen bound.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"231 ","pages":"Article 110628"},"PeriodicalIF":0.7,"publicationDate":"2025-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841475","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 : 2025-12-18DOI: 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":"2025-12-18","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 : 2025-12-18DOI: 10.1016/j.spl.2025.110625
Shengli Zhao, Min Han, Zhaohui Yan
This paper introduces the -pattern, which is used to rank the columns of a baseline design, and proposes the minimum individual aberration (MIA) criterion for selecting baseline designs. We present an algorithm for completely searching MIA baseline designs using two-level orthogonal arrays. MIA baseline designs with run sizes of 8, 12, 16, and 20 are tabulated. Finally, we propose a partial order to rank the columns of a baseline design by their confounding severity.
{"title":"Minimum individual aberration two-level baseline designs","authors":"Shengli Zhao, Min Han, Zhaohui Yan","doi":"10.1016/j.spl.2025.110625","DOIUrl":"10.1016/j.spl.2025.110625","url":null,"abstract":"<div><div>This paper introduces the <span><math><mi>δ</mi></math></span>-pattern, which is used to rank the columns of a baseline design, and proposes the minimum individual aberration (MIA) criterion for selecting baseline designs. We present an algorithm for completely searching MIA baseline designs using two-level orthogonal arrays. MIA baseline designs with run sizes of 8, 12, 16, and 20 are tabulated. Finally, we propose a partial order to rank the columns of a baseline design by their confounding severity.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"231 ","pages":"Article 110625"},"PeriodicalIF":0.7,"publicationDate":"2025-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145792041","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 : 2025-12-17DOI: 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":"2025-12-17","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 : 2025-12-15DOI: 10.1016/j.spl.2025.110622
Lorenzo Camponovo
We study the relationship between stochastic and deterministic polynomial trends over the long-run, as the sample size , and at a local level, by focusing on the last observations of the sample, with . First, we show that stochastic processes with integration order , for integer , locally behave like deterministic polynomial trend models of degree , scaled by asymptotically normal random variables that are constants at a local level. Second, we introduce statistical procedures to determine the order of polynomial trend models, thereby providing an indirect way to assess integration in stochastic processes. Using data on fourteen major U.S. macroeconomic variables, our method confirms that most are , while Money Stock and Bond Yields exhibit , highlighting the effectiveness of our approach in detecting higher-order integration.
{"title":"On the relationship between stochastic and deterministic polynomial trends with applications to the detection of the order of integration","authors":"Lorenzo Camponovo","doi":"10.1016/j.spl.2025.110622","DOIUrl":"10.1016/j.spl.2025.110622","url":null,"abstract":"<div><div>We study the relationship between stochastic and deterministic polynomial trends over the long-run, as the sample size <span><math><mrow><mi>N</mi><mo>→</mo><mi>∞</mi></mrow></math></span>, and at a local level, by focusing on the last <span><math><mi>n</mi></math></span> observations of the sample, with <span><math><mrow><mi>n</mi><mo>=</mo><mi>o</mi><mrow><mo>(</mo><mi>N</mi><mo>)</mo></mrow></mrow></math></span>. First, we show that stochastic processes with integration order <span><math><mrow><mi>I</mi><mrow><mo>(</mo><mi>d</mi><mo>)</mo></mrow></mrow></math></span>, for integer <span><math><mrow><mi>d</mi><mo>≥</mo><mn>1</mn></mrow></math></span>, locally behave like deterministic polynomial trend models of degree <span><math><mrow><mi>d</mi><mo>−</mo><mn>1</mn></mrow></math></span>, scaled by asymptotically normal random variables that are constants at a local level. Second, we introduce statistical procedures to determine the order of polynomial trend models, thereby providing an indirect way to assess integration in stochastic processes. Using data on fourteen major U.S. macroeconomic variables, our method confirms that most are <span><math><mrow><mi>I</mi><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>, while Money Stock and Bond Yields exhibit <span><math><mrow><mi>I</mi><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></mrow></math></span>, highlighting the effectiveness of our approach in detecting higher-order integration.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"231 ","pages":"Article 110622"},"PeriodicalIF":0.7,"publicationDate":"2025-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145792043","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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