Pub Date : 2025-11-17DOI: 10.1016/j.spl.2025.110602
Doudou Li , Han Liu , Mei Zhang
In this paper, we consider a subcritical Galton–Watson branching process with state-dependent immigration , where immigration is allowed to enter iff the previous generation was empty. Under the exponential moment conditions of branching and immigration, we obtain the large deviations rate of the total population of up to time .
{"title":"Large deviations for a subcritical Galton–Watson process with state-dependent immigration","authors":"Doudou Li , Han Liu , Mei Zhang","doi":"10.1016/j.spl.2025.110602","DOIUrl":"10.1016/j.spl.2025.110602","url":null,"abstract":"<div><div>In this paper, we consider a subcritical Galton–Watson branching process with state-dependent immigration <span><math><mi>X</mi></math></span>, where immigration is allowed to enter iff the previous generation was empty. Under the exponential moment conditions of branching and immigration, we obtain the large deviations rate of the total population of <span><math><mi>X</mi></math></span> up to time <span><math><mi>n</mi></math></span>.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"230 ","pages":"Article 110602"},"PeriodicalIF":0.7,"publicationDate":"2025-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145624244","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 : 2025-11-14DOI: 10.1016/j.spl.2025.110592
Ronald Ortner
Given a unichain Markov reward process (MRP), we provide an explicit expression for the bias values in terms of mean first passage times. This result implies a generalization of known Markov chain perturbation bounds for the stationary distribution to the case where the perturbed chain is not irreducible. It further yields an improved perturbation bound in 1-norm. As a special case, Kemeny’s constant can be interpreted as the translated bias in an MRP with constant reward , which offers an intuitive explanation why it is a constant.
{"title":"An identity for the bias in Markov reward processes with applications to Markov chain perturbation and Kemeny’s constant","authors":"Ronald Ortner","doi":"10.1016/j.spl.2025.110592","DOIUrl":"10.1016/j.spl.2025.110592","url":null,"abstract":"<div><div>Given a unichain Markov reward process (MRP), we provide an explicit expression for the bias values in terms of mean first passage times. This result implies a generalization of known Markov chain perturbation bounds for the stationary distribution to the case where the perturbed chain is not irreducible. It further yields an improved perturbation bound in 1-norm. As a special case, Kemeny’s constant can be interpreted as the translated bias in an MRP with constant reward <span><math><mrow><mo>−</mo><mn>1</mn></mrow></math></span>, which offers an intuitive explanation why it is a constant.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"230 ","pages":"Article 110592"},"PeriodicalIF":0.7,"publicationDate":"2025-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145580287","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 : 2025-11-11DOI: 10.1016/j.spl.2025.110589
Catia Scricciolo
We study the problem of deconvolving an unknown distribution function when the error distribution is ordinary smooth and unknown. Using data from an auxiliary experiment that provides information about the error distribution, we establish minimax-optimal convergence rates (up to logarithmic factors) with respect to the 1-Wasserstein metric for a kernel-based distribution function estimator over the full range of Hölder-type classes of densities on . Furthermore, we propose a rate-adaptive, data-driven estimation procedure that automatically selects the optimal bandwidth across -Hölder-type classes of mixing densities for , requiring no prior knowledge of the regularity parameters.
{"title":"Adaptive minimax-optimal Wasserstein deconvolution with unknown error distributions","authors":"Catia Scricciolo","doi":"10.1016/j.spl.2025.110589","DOIUrl":"10.1016/j.spl.2025.110589","url":null,"abstract":"<div><div>We study the problem of deconvolving an unknown distribution function when the error distribution is ordinary smooth and unknown. Using data from an auxiliary experiment that provides information about the error distribution, we establish minimax-optimal convergence rates (up to logarithmic factors) with respect to the 1-Wasserstein metric for a kernel-based distribution function estimator over the full range of Hölder-type classes of densities on <span><math><mi>R</mi></math></span>. Furthermore, we propose a rate-adaptive, data-driven estimation procedure that automatically selects the optimal bandwidth across <span><math><mi>α</mi></math></span>-Hölder-type classes of mixing densities for <span><math><mrow><mi>α</mi><mo>≥</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></math></span>, requiring no prior knowledge of the regularity parameters.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"230 ","pages":"Article 110589"},"PeriodicalIF":0.7,"publicationDate":"2025-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145529166","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 : 2025-11-04DOI: 10.1016/j.spl.2025.110588
M.C. Jones
Gaunt (2026) introduced and studied the non-central chi-squared difference distribution. One version of this arose as the distribution of the product of the two marginal random variables of the general (non-degenerate) bivariate normal distribution. Initially, I provide an alternative basic argument as to why this is so. The main focus of the article, however, is to extend a number of known mixing relationships between (non-central) chi-squared distributions to the (non-central) chi-squared difference distribution case. In certain circumstances, just a single mixing random variable remains required rather than the two independent ones that are trivially applicable in general.
{"title":"On mixture relationships between central and non-central chi-squared difference distributions","authors":"M.C. Jones","doi":"10.1016/j.spl.2025.110588","DOIUrl":"10.1016/j.spl.2025.110588","url":null,"abstract":"<div><div>Gaunt (2026) introduced and studied the non-central chi-squared difference distribution. One version of this arose as the distribution of the product of the two marginal random variables of the general (non-degenerate) bivariate normal distribution. Initially, I provide an alternative basic argument as to why this is so. The main focus of the article, however, is to extend a number of known mixing relationships between (non-central) chi-squared distributions to the (non-central) chi-squared difference distribution case. In certain circumstances, just a single mixing random variable remains required rather than the two independent ones that are trivially applicable in general.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"229 ","pages":"Article 110588"},"PeriodicalIF":0.7,"publicationDate":"2025-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145466737","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 : 2025-10-27DOI: 10.1016/j.spl.2025.110581
Jie Zhang , Yang Liu , Qian Sun
We propose a maximum conditional likelihood estimation approach for the random encounter and staying time model, incorporating simulation-extrapolation to correct for biases arising from measurement error. The effectiveness of proposed methods is demonstrated via simulations and field data.
{"title":"Maximum conditional likelihood estimation for the REST model with measurement error","authors":"Jie Zhang , Yang Liu , Qian Sun","doi":"10.1016/j.spl.2025.110581","DOIUrl":"10.1016/j.spl.2025.110581","url":null,"abstract":"<div><div>We propose a maximum conditional likelihood estimation approach for the random encounter and staying time model, incorporating simulation-extrapolation to correct for biases arising from measurement error. The effectiveness of proposed methods is demonstrated via simulations and field data.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"229 ","pages":"Article 110581"},"PeriodicalIF":0.7,"publicationDate":"2025-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145419173","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 : 2025-10-24DOI: 10.1016/j.spl.2025.110574
Peter Grünwald , Wouter M. Koolen
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 -test and sequential linear regression with nuisance covariates.
{"title":"Supermartingales for one-sided tests: Sufficient monotone likelihood ratios are sufficient","authors":"Peter Grünwald , 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":"2025-10-24","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}
Pub Date : 2025-10-22DOI: 10.1016/j.spl.2025.110580
Hongchao Qian
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.
{"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":"2025-10-22","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}
Pub Date : 2025-10-18DOI: 10.1016/j.spl.2025.110579
Manabu Asai
This paper utilizes the Bartlett decomposition of a singular Wishart variable to derive the log-expectation. A re-parameterization for maximum likelihood estimation is proposed to separately estimate the scale matrix and the degrees-of-freedom parameter. Its asymptotic and finite-sample properties are investigated.
{"title":"Maximum likelihood estimation for singular Wishart distributions","authors":"Manabu Asai","doi":"10.1016/j.spl.2025.110579","DOIUrl":"10.1016/j.spl.2025.110579","url":null,"abstract":"<div><div>This paper utilizes the Bartlett decomposition of a singular Wishart variable to derive the log-expectation. A re-parameterization for maximum likelihood estimation is proposed to separately estimate the scale matrix and the degrees-of-freedom parameter. Its asymptotic and finite-sample properties are investigated.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"229 ","pages":"Article 110579"},"PeriodicalIF":0.7,"publicationDate":"2025-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145360125","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 : 2025-10-18DOI: 10.1016/j.spl.2025.110578
Yan Zhu , Shanqi Pang , Xiao Lin , Chen Li
This paper investigates asymmetric orthogonal arrays with seven factors of strength two and presents a few new constructions. The proposed method is straightforward and constructive. We obtain numerous infinite families of such arrays. Selective arrays are tabulated for practical uses.
{"title":"The existence of a class of asymmetric orthogonal arrays with seven factors","authors":"Yan Zhu , Shanqi Pang , Xiao Lin , Chen Li","doi":"10.1016/j.spl.2025.110578","DOIUrl":"10.1016/j.spl.2025.110578","url":null,"abstract":"<div><div>This paper investigates asymmetric orthogonal arrays with seven factors of strength two and presents a few new constructions. The proposed method is straightforward and constructive. We obtain numerous infinite families of such arrays. Selective arrays are tabulated for practical uses.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"229 ","pages":"Article 110578"},"PeriodicalIF":0.7,"publicationDate":"2025-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145365342","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 : 2025-10-18DOI: 10.1016/j.spl.2025.110577
Wouter M. Koolen , Muriel F. Pérez-Ortiz , Tyron Lardy
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.
{"title":"A generalisation of Ville’s inequality to monotonic lower bounds and thresholds","authors":"Wouter M. Koolen , Muriel F. Pérez-Ortiz , 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":"2025-10-18","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}
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