Statistics & Probability Letters最新文献

{"title":"Mean reflected backward stochastic partial differential equations","authors":"Hongchao Qian","doi":"10.1016/j.spl.2025.110580","DOIUrl":"10.1016/j.spl.2025.110580","url":null,"abstract":"<div><div>This paper is concerned with a class of one-dimensional mean reflected backward stochastic partial differential equations (MRBSPDEs). In our framework, the constraint depends on the law of the solution rather than on its paths. Specifically, the compensating reflection part keeps the expectation of the solution above a given deterministic function. The existence and uniqueness of solution are established by a penalty method.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"229 ","pages":"Article 110580"},"PeriodicalIF":0.7,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145365200","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}

{"title":"A generalisation of Ville’s inequality to monotonic lower bounds and thresholds","authors":"Wouter M. Koolen ,&nbsp;Muriel F. Pérez-Ortiz ,&nbsp;Tyron Lardy","doi":"10.1016/j.spl.2025.110577","DOIUrl":"10.1016/j.spl.2025.110577","url":null,"abstract":"<div><div>Essentially all anytime-valid methods hinge on Ville’s inequality to gain validity across time without incurring a union bound. Ville’s inequality is a proper generalisation of Markov’s inequality. It states that a non-negative supermartingale will only ever reach a multiple of its initial value with small probability. In the classic rendering both the lower bound (of zero) and the threshold are constant in time. We generalise both to monotonic curves. That is, we bound the probability that a supermartingale which remains above a given decreasing curve exceeds a given increasing threshold curve. We show our bound is tight by exhibiting a supermartingale for which the bound is an equality. Using our generalisation, we derive a cleaner finite-time version of the law of the iterated logarithm.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"229 ","pages":"Article 110577"},"PeriodicalIF":0.7,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145365343","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}

{"title":"Supermartingales for one-sided tests: Sufficient monotone likelihood ratios are sufficient","authors":"Peter Grünwald ,&nbsp;Wouter M. Koolen","doi":"10.1016/j.spl.2025.110574","DOIUrl":"10.1016/j.spl.2025.110574","url":null,"abstract":"<div><div>The t-statistic is a widely-used scale-invariant statistic for testing the null hypothesis that the mean is zero. Martingale methods enable sequential testing with the t-statistic at every sample size, while controlling the probability of falsely rejecting the null. For one-sided sequential tests, which reject when the t-statistic is too positive, a natural question is whether they also control false rejection when the true mean is negative. We prove that this is the case using monotone likelihood ratios and sufficient statistics. We develop applications to the scale-invariant t-test, the location-invariant <span><math><msup><mrow><mi>χ</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-test and sequential linear regression with nuisance covariates.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"229 ","pages":"Article 110574"},"PeriodicalIF":0.7,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145466738","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}

{"title":"A note on blinded continuous monitoring for continuous outcomes","authors":"Long-Hao Xu,&nbsp;Tim Friede","doi":"10.1016/j.spl.2025.110575","DOIUrl":"10.1016/j.spl.2025.110575","url":null,"abstract":"<div><div>Continuous monitoring is becoming more popular due to its significant benefits, including reducing sample sizes and reaching earlier conclusions. In general, it involves monitoring nuisance parameters (e.g., the variance of outcomes) until a specific condition is satisfied. The blinded method, which does not require revealing group assignments, was recommended because it maintains the integrity of the experiment and mitigates potential bias. Although Friede and Miller (2012) investigated the characteristics of blinded continuous monitoring through simulation studies, its theoretical properties are not fully explored. In this paper, we aim to fill this gap by presenting the asymptotic and finite-sample properties of the blinded continuous monitoring for continuous outcomes. Furthermore, we examine the impact of using blinded versus unblinded variance estimators in the context of continuous monitoring. Simulation results are also provided to evaluate finite-sample performance and to support the theoretical findings.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"228 ","pages":"Article 110575"},"PeriodicalIF":0.7,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145321939","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}

{"title":"Variance-based difference between graphical identification conditions of causal effects in linear structural equation models","authors":"Chie Taguchi ,&nbsp;Manabu Kuroki","doi":"10.1016/j.spl.2025.110561","DOIUrl":"10.1016/j.spl.2025.110561","url":null,"abstract":"<div><div>In the context of statistical causal inference using linear structural equation models, researchers in the field of artificial intelligence and statistical science have developed several identification conditions for evaluating causal effects. However, there are some scenarios where several identification conditions can be applied simultaneously to estimate causal effects. To enhance estimation accuracy, we focus on five key identification conditions: the back-door criterion, the front-door criterion, the front-door-like criterion, the conditional instrumental variable condition, and the effect restoration condition. We then compare these five identification conditions in terms of estimation accuracy (asymptotic variance) and conclude that, in some cases, the qualitative comparison of estimation accuracy among these identification conditions can be directly assessed from the graphical structure, even before statistical data are collected.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"228 ","pages":"Article 110561"},"PeriodicalIF":0.7,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145321940","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}

{"title":"Iterated ergodic theorems and Erdös–Rényi law of large numbers","authors":"Yuri Kifer","doi":"10.1016/j.spl.2025.110572","DOIUrl":"10.1016/j.spl.2025.110572","url":null,"abstract":"<div><div>We obtain ergodic theorems and a version of the Erdös–Rènyi law of large numbers for multiple iterated sums and integrals of the form <span><math><mrow><msup><mrow><mi>Σ</mi></mrow><mrow><mrow><mo>(</mo><mi>ν</mi><mo>)</mo></mrow></mrow></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><msub><mrow><mo>∑</mo></mrow><mrow><mn>0</mn><mo>≤</mo><msub><mrow><mi>k</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>&lt;</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>&lt;</mo><msub><mrow><mi>k</mi></mrow><mrow><mi>ν</mi></mrow></msub><mo>≤</mo><mi>t</mi></mrow></msub><mi>ξ</mi><mrow><mo>(</mo><msub><mrow><mi>k</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo></mrow><mo>⊗</mo><mo>⋯</mo><mo>⊗</mo><mi>ξ</mi><mrow><mo>(</mo><msub><mrow><mi>k</mi></mrow><mrow><mi>ν</mi></mrow></msub><mo>)</mo></mrow></mrow></math></span>, <span><math><mrow><mi>t</mi><mo>∈</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>]</mo></mrow></mrow></math></span> and <span><math><mrow><msup><mrow><mi>Σ</mi></mrow><mrow><mrow><mo>(</mo><mi>ν</mi><mo>)</mo></mrow></mrow></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><msub><mrow><mo>∫</mo></mrow><mrow><mn>0</mn><mo>≤</mo><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>≤</mo><mo>⋯</mo><mo>≤</mo><msub><mrow><mi>s</mi></mrow><mrow><mi>ν</mi></mrow></msub><mo>≤</mo><mi>t</mi></mrow></msub><mi>ξ</mi><mrow><mo>(</mo><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo></mrow><mo>⊗</mo><mo>⋯</mo><mo>⊗</mo><mi>ξ</mi><mrow><mo>(</mo><msub><mrow><mi>s</mi></mrow><mrow><mi>ν</mi></mrow></msub><mo>)</mo></mrow><mi>d</mi><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>⋯</mo><mi>d</mi><msub><mrow><mi>s</mi></mrow><mrow><mi>ν</mi></mrow></msub></mrow></math></span> where <span><math><msub><mrow><mrow><mo>{</mo><mi>ξ</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow><mo>}</mo></mrow></mrow><mrow><mo>−</mo><mi>∞</mi><mo>&lt;</mo><mi>k</mi><mo>&lt;</mo><mi>∞</mi></mrow></msub></math></span> and <span><math><msub><mrow><mrow><mo>{</mo><mi>ξ</mi><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow><mo>}</mo></mrow></mrow><mrow><mo>−</mo><mi>∞</mi><mo>&lt;</mo><mi>s</mi><mo>&lt;</mo><mi>∞</mi></mrow></msub></math></span> are stationary vector stochastic processes.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"228 ","pages":"Article 110572"},"PeriodicalIF":0.7,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222580","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}

{"title":"Change-point detection in Vector-Tensor linear model","authors":"Haiyue Su ,&nbsp;Zhiming Xia ,&nbsp;Wenyuan Shang ,&nbsp;Meili Shi","doi":"10.1016/j.spl.2025.110563","DOIUrl":"10.1016/j.spl.2025.110563","url":null,"abstract":"<div><div>For high-throughput low-rank data, CANDECOMP/PARAFAC (<span><math><mi>CP</mi></math></span>) decomposition is frequently employed to reduce the dimensionality to a manageable level. In this article, we consider a Vector-Tensor linear regression model, where the low-rank structure is expressed through CP decomposition, and the change-point structure is incorporated into the multi-array coefficients. A novel procedure is proposed to jointly detect the change-point and estimate the tensor structure by minimizing the sum of squared residuals. The associated algorithm is developed based on Alternating Least Squares (ALS) algorithm, and is computationally efficient and scalable. Furthermore, we establish the consistency of the change-point estimator under a set of general conditions. Simulations and empirical studies illustrate the validity and effectiveness.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"228 ","pages":"Article 110563"},"PeriodicalIF":0.7,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222582","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}

{"title":"Uniform mean estimation for monotonic processes","authors":"Eugenio Clerico ,&nbsp;Hamish E. Flynn ,&nbsp;Patrick Rebeschini","doi":"10.1016/j.spl.2025.110558","DOIUrl":"10.1016/j.spl.2025.110558","url":null,"abstract":"<div><div>We consider the problem of deriving uniform confidence bands for the mean of a monotonic stochastic process, such as the cumulative distribution function (CDF) of a random variable, based on a sequence of i.i.d. observations. Our approach leverages the coin-betting framework, and inherits several favourable characteristics of coin-betting methods. In particular, for each point in the domain of the mean function, we obtain anytime-valid confidence intervals that are numerically tight and adapt to the variance of the observations. To derive uniform confidence bands, we employ a continuous union bound that crucially leverages monotonicity. In the case of CDF estimation, we also exploit the fact that the empirical CDF is piece-wise constant to obtain simple confidence bands that can be easily computed. In simulations, we find that our confidence bands for the CDF achieve state-of-the-art performance.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"228 ","pages":"Article 110558"},"PeriodicalIF":0.7,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145160353","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}

{"title":"Double dipping with balanced sampling","authors":"Blair Robertson,&nbsp;Chris Price,&nbsp;Marco Reale","doi":"10.1016/j.spl.2025.110562","DOIUrl":"10.1016/j.spl.2025.110562","url":null,"abstract":"<div><div>Doubly balanced samples from spatial populations have approximate balance on auxiliary variables and spread over spatial coordinates. This article shows that doubly balanced sampling is also efficient on non-spatial populations when we balance on auxiliary variables and spread over the space spanned by them. Numerical results on three example applications show that our extension of doubly balanced sampling works well in practice.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"228 ","pages":"Article 110562"},"PeriodicalIF":0.7,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145160357","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}

{"title":"Multiple testing in generalized universal inference","authors":"Neil Dey,&nbsp;Ryan Martin,&nbsp;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":"2026-02-01","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}