Pub Date : 2025-11-19DOI: 10.1016/j.spl.2025.110603
Diana Rauwolf , Udo Kamps
For renewal processes with random time, extensions of well-known asymptotic relations such as the elementary renewal theorem, Blackwell’s renewal and Smith’s key renewal theorem are given. Whereas, in these results, time tends to infinity, the limits here are taken with respect to a sequence of parameters of respective random-time distributions satisfying some condition.
{"title":"Asymptotic behavior of renewal processes with random time","authors":"Diana Rauwolf , Udo Kamps","doi":"10.1016/j.spl.2025.110603","DOIUrl":"10.1016/j.spl.2025.110603","url":null,"abstract":"<div><div>For renewal processes with random time, extensions of well-known asymptotic relations such as the elementary renewal theorem, Blackwell’s renewal and Smith’s key renewal theorem are given. Whereas, in these results, time tends to infinity, the limits here are taken with respect to a sequence of parameters of respective random-time distributions satisfying some condition.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"230 ","pages":"Article 110603"},"PeriodicalIF":0.7,"publicationDate":"2025-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145580286","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 : 2025-11-17DOI: 10.1016/j.spl.2025.110590
Louis Deutsch, Eugene Katsevich
We investigate inference in a latent binary variable model where a noisy proxy of the latent variable is available, motivated by the variable perturbation effectiveness problem in single-cell CRISPR screens. The baseline approach is to ignore the perturbation effectiveness problem, while a recent proposal employs a weighted average based on the proxies. Our main goals are to determine how accurate the proxies must be in order for a weighted test to gain power over the unweighted baseline, and to develop tests that are powerful regardless of the accuracy of the proxies. To address the first goal, we compute the Pitman relative efficiency of the weighted test relative to the unweighted test, yielding an interpretable quantification of proxy quality that drives the power of the weighted test. To address the second goal, we propose two strategies. First, we propose a maximum-likelihood based approach that adapts the proxies to the data. Second, we propose an estimator of the Pitman efficiency if a “positive control outcome variable” is available (as is often the case in single-cell CRISPR screens), which facilitates an adaptive choice of whether to use the proxies at all. Our numerical simulations support the Pitman efficiency as the key quantity for determining whether the weighted test gains power over the baseline, and demonstrate that the two proposed adaptive tests can improve on both existing approaches across a range of proxy qualities.
{"title":"Location tests with noisy proxies for latent variables","authors":"Louis Deutsch, Eugene Katsevich","doi":"10.1016/j.spl.2025.110590","DOIUrl":"10.1016/j.spl.2025.110590","url":null,"abstract":"<div><div>We investigate inference in a latent binary variable model where a noisy proxy of the latent variable is available, motivated by the variable perturbation effectiveness problem in single-cell CRISPR screens. The baseline approach is to ignore the perturbation effectiveness problem, while a recent proposal employs a weighted average based on the proxies. Our main goals are to determine how accurate the proxies must be in order for a weighted test to gain power over the unweighted baseline, and to develop tests that are powerful regardless of the accuracy of the proxies. To address the first goal, we compute the Pitman relative efficiency of the weighted test relative to the unweighted test, yielding an interpretable quantification of proxy quality that drives the power of the weighted test. To address the second goal, we propose two strategies. First, we propose a maximum-likelihood based approach that adapts the proxies to the data. Second, we propose an estimator of the Pitman efficiency if a “positive control outcome variable” is available (as is often the case in single-cell CRISPR screens), which facilitates an adaptive choice of whether to use the proxies at all. Our numerical simulations support the Pitman efficiency as the key quantity for determining whether the weighted test gains power over the baseline, and demonstrate that the two proposed adaptive tests can improve on both existing approaches across a range of proxy qualities.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"230 ","pages":"Article 110590"},"PeriodicalIF":0.7,"publicationDate":"2025-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145580285","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 : 2025-11-17DOI: 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}
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