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}
Pub Date : 2025-10-17DOI: 10.1016/j.spl.2025.110576
Longxiang Fang , Yu Ruan , N. Balakrishnan
Stochastic comparisons are quite helpful in optimizing system designs by evaluating the performance of different configurations and ensuring that critical systems meet reliability standards under diverse conditions. In this paper, we discuss stochastic comparisons of lifetimes of two-series–parallel systems with independent components randomly chosen from two different batches. We assume the components from the first batch is more reliable than the components from the second batch. Then, in the case of two-series–parallel system, we prove that the reliability of the system increases in terms of the usual stochastic order, as the random number, , taking values in , of components chosen from the first batch increases in increasing concave order or the random number, , taking values in , of components chosen from the first batch decreases in increasing convex order. We also present some numerical examples to illustrate all the results established here.
{"title":"Stochastic comparisons of two-series–parallel systems with independent components randomly chosen from two batches","authors":"Longxiang Fang , Yu Ruan , N. Balakrishnan","doi":"10.1016/j.spl.2025.110576","DOIUrl":"10.1016/j.spl.2025.110576","url":null,"abstract":"<div><div>Stochastic comparisons are quite helpful in optimizing system designs by evaluating the performance of different configurations and ensuring that critical systems meet reliability standards under diverse conditions. In this paper, we discuss stochastic comparisons of lifetimes of two-series–parallel systems with <span><math><mrow><mn>2</mn><mi>n</mi></mrow></math></span> independent components randomly chosen from two different batches. We assume the <span><math><mi>n</mi></math></span> components from the first batch is more reliable than the <span><math><mi>n</mi></math></span> components from the second batch. Then, in the case of two-series–parallel system, we prove that the reliability of the system increases in terms of the usual stochastic order, as the random number, <span><math><mi>K</mi></math></span>, taking values in <span><math><mrow><mo>{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mrow><mo>[</mo><mfrac><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>]</mo></mrow><mo>}</mo></mrow></math></span>, of components chosen from the first batch increases in increasing concave order or the random number, <span><math><mi>K</mi></math></span>, taking values in <span><math><mrow><mo>{</mo><mrow><mo>[</mo><mfrac><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>]</mo></mrow><mo>+</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>n</mi><mo>}</mo></mrow></math></span>, of components chosen from the first batch decreases in increasing convex order. We also present some numerical examples to illustrate all the results established here.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"229 ","pages":"Article 110576"},"PeriodicalIF":0.7,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145324181","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 : 2025-10-11DOI: 10.1016/j.spl.2025.110575
Long-Hao Xu, Tim Friede
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.
{"title":"A note on blinded continuous monitoring for continuous outcomes","authors":"Long-Hao Xu, 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":"2025-10-11","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}
Pub Date : 2025-10-10DOI: 10.1016/j.spl.2025.110561
Chie Taguchi , Manabu Kuroki
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.
{"title":"Variance-based difference between graphical identification conditions of causal effects in linear structural equation models","authors":"Chie Taguchi , 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":"2025-10-10","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}
Pub Date : 2025-10-04DOI: 10.1016/j.spl.2025.110573
Xin-Yi Xu , Jiang-Feng Wang , Kang Hu , Shan He , Yu Xia
This paper investigates the asymptotic properties of local linear quantile regression estimators for spatial data generated by strictly stationary and associated spatial processes . We study local linear estimators for both the conditional quantile function and its first-order partial derivatives. Under appropriate regularity conditions, we derive the Bahadur representation for these estimators, which is utilized to establish their joint asymptotic normality. To assess finite-sample performance, we conduct Monte Carlo simulations in a two-dimensional space (). The results demonstrate the applicability of the proposed estimators and confirm the theoretical asymptotic properties.
{"title":"Spatial local linear quantile regression under association","authors":"Xin-Yi Xu , Jiang-Feng Wang , Kang Hu , Shan He , Yu Xia","doi":"10.1016/j.spl.2025.110573","DOIUrl":"10.1016/j.spl.2025.110573","url":null,"abstract":"<div><div>This paper investigates the asymptotic properties of local linear quantile regression estimators for spatial data generated by strictly stationary and associated spatial processes <span><math><mrow><mo>{</mo><mrow><mo>(</mo><msub><mrow><mi>Y</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>)</mo></mrow><mo>,</mo><mi>i</mi><mo>∈</mo><msup><mrow><mi>Z</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>}</mo></mrow></math></span>. We study local linear estimators for both the conditional quantile function <span><math><mrow><msub><mrow><mi>q</mi></mrow><mrow><mi>p</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> and its first-order partial derivatives. Under appropriate regularity conditions, we derive the Bahadur representation for these estimators, which is utilized to establish their joint asymptotic normality. To assess finite-sample performance, we conduct Monte Carlo simulations in a two-dimensional space (<span><math><mrow><mi>N</mi><mo>=</mo><mn>2</mn></mrow></math></span>). The results demonstrate the applicability of the proposed estimators and confirm the theoretical asymptotic properties.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"228 ","pages":"Article 110573"},"PeriodicalIF":0.7,"publicationDate":"2025-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145269905","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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