{"title":"Estimation of the optimal treatment regimes with multiple treatments under proportional hazards model","authors":"Yuexin Fang , Xiangyong Tan , Qian Li","doi":"10.1016/j.spl.2025.110357","DOIUrl":"10.1016/j.spl.2025.110357","url":null,"abstract":"<div><div>We propose a novel proportional hazards model that include an unknown baseline covariate effect and the interaction between multiple treatments and covariates on censored survival data. Doubly robust estimating equations constructed by utilizing the A-learning methodology and time-dependent propensity score. The asymptotic properties of the proposed estimators are established under the correct specification of either the baseline effect model or the propensity score model. Extensive simulation studies, along with an application, demonstrate the efficacy of the proposed approach.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110357"},"PeriodicalIF":0.9,"publicationDate":"2025-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143161560","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":"Sylvester’s problem for random walks and bridges","authors":"Hugo Panzo","doi":"10.1016/j.spl.2024.110349","DOIUrl":"10.1016/j.spl.2024.110349","url":null,"abstract":"<div><div>Consider a random walk in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> that starts at the origin and whose increment distribution assigns zero probability to any affine hyperplane. We solve Sylvester’s problem for these random walks by showing that the probability that any <span><math><mrow><mi>d</mi><mo>+</mo><mn>2</mn></mrow></math></span> consecutive steps of the walk are in convex position is equal to <span><math><mrow><mn>1</mn><mo>−</mo><mfrac><mrow><mn>2</mn></mrow><mrow><mrow><mo>(</mo><mi>d</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mo>!</mo></mrow></mfrac></mrow></math></span>. The analogous result also holds for random bridges of length at least <span><math><mrow><mi>d</mi><mo>+</mo><mn>2</mn></mrow></math></span> whose joint increment distribution is exchangeable.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110349"},"PeriodicalIF":0.9,"publicationDate":"2025-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143161558","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":"Choice of the hypothesis matrix for using the Anova-type-statistic","authors":"Paavo Sattler , Manuel Rosenbaum","doi":"10.1016/j.spl.2025.110356","DOIUrl":"10.1016/j.spl.2025.110356","url":null,"abstract":"<div><div>Initially developed in <span><span>Brunner et al. (1997)</span></span>, the Anova-type-statistic (ATS) is one of the most used quadratic forms for testing multivariate hypotheses for a variety of different parameter vectors <span><math><mrow><mi>θ</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></mrow></math></span>. Tests based on a version of the ATS are usually preferable over those based on other quadratic forms, like the Wald-type-statistic. However, the same null hypothesis <span><math><mrow><mi>H</mi><mi>θ</mi><mo>=</mo><mi>y</mi></mrow></math></span> can be expressed by various hypothesis matrices <span><math><mrow><mi>H</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>m</mi><mo>×</mo><mi>d</mi></mrow></msup></mrow></math></span> and corresponding vectors <span><math><mrow><mi>y</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>m</mi></mrow></msup></mrow></math></span>, yielding different values of the test statistic. Since this can entail differing test decisions, we investigate under which conditions certain tests using different hypothesis matrices coincide. In this manuscript, we show that for several versions of the Anova-type-statistic, for each hypothesis <span><math><mrow><mi>H</mi><mi>θ</mi><mo>=</mo><mi>y</mi></mrow></math></span> a companion matrix with a minimal number of rows can be constructed, testing the same hypothesis but also always yielding the same test decisions. This can substantially reduce computation time, as demonstrated in several conducted simulations.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110356"},"PeriodicalIF":0.9,"publicationDate":"2025-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143161559","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Construction of asymmetric resolvable orthogonal arrays","authors":"Xiao Lin, Shanqi Pang","doi":"10.1016/j.spl.2025.110355","DOIUrl":"10.1016/j.spl.2025.110355","url":null,"abstract":"<div><div>Asymmetric resolvable orthogonal arrays have received more and more attention in experimental design, computer experiments, multiple experiments, cross validation, stochastic optimization, and quantum information. However, there are extremely few constructions of asymmetric resolvable orthogonal arrays. This article generalizes the definition of asymmetric resolvable orthogonal arrays and presents some approaches for constructing such arrays.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110355"},"PeriodicalIF":0.9,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143161523","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":"Some general points for inflation models","authors":"Dankmar Böhning , Sunisa Junnumtuam","doi":"10.1016/j.spl.2024.110346","DOIUrl":"10.1016/j.spl.2024.110346","url":null,"abstract":"<div><div>This paper presents a general approach to inflation models with an arbitrary number of inflation points. Using the convex theory of discrete mixture models it achieves some general results including closed form expressions for the estimates of the inflation weights and separability of the likelihood.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110346"},"PeriodicalIF":0.9,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143161524","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Sparse inverse covariance selection with mass-nonlocal priors","authors":"Taiwo Fagbohungbe , Liangliang Zhang , Xuan Cao","doi":"10.1016/j.spl.2024.110348","DOIUrl":"10.1016/j.spl.2024.110348","url":null,"abstract":"<div><div>To tackle the challenges of understanding complex multivariate relationships in high-dimensional settings, we develop a method for estimating the sparsity pattern of inverse covariance matrices. Our approach employs a generalized likelihood framework for scalable computation, integrating spike and slab priors with nonlocal slab components on the elements of the inverse covariance matrix. We implement the Bayesian model using an entry-wise Gibbs sampler and establish its theoretical consistency in high-dimensional settings under mild conditions. The practical utility of our method is demonstrated through extensive numerical studies and an application to neuropathy data analysis.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110348"},"PeriodicalIF":0.9,"publicationDate":"2025-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143161016","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":"Differentially private histogram with valid statistics","authors":"Zilong Cao , Shisong Wu , Xuanang Li , Hai Zhang","doi":"10.1016/j.spl.2024.110354","DOIUrl":"10.1016/j.spl.2024.110354","url":null,"abstract":"<div><div>Differentially private histograms (DP-Histograms) are integral to data publication and privacy preservation efforts. However, conventional DP-Histograms often fail to preserve valid statistical information and the essential characteristics of the original data. This paper shows the invalidity of variance is the inherent shortcomings in general DP-Histograms, and introduces a novel algorithm called the Differentially Private Histogram with Valid Statistics (VSDPH) to overcome the problem. The VSDPH, grounded in linear programming and bounded Lipschitz distance, efficiently generates DP histograms while preserving the valid statistics of the original data. Our theoretical analysis demonstrates that histograms produced by VSDPH maintain asymptotically valid variance, and we establish an upper bound based on the 1-Wasserstein distance. Through experiments, we validate that VSDPH can accurately hold the statistical characteristics of the original data. This capability brings the resulting histograms closer to the originals.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110354"},"PeriodicalIF":0.9,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143161557","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":"Matrix reshaping for statistics","authors":"Nicola Loperfido","doi":"10.1016/j.spl.2024.110347","DOIUrl":"10.1016/j.spl.2024.110347","url":null,"abstract":"<div><div>The reshaping of a block matrix vectorizes, transposes and stacks on top of each other the blocks of the matrix itself. This paper investigates the statistical applications of matrix reshaping to three-way data, partial traces and measures of multivariate shape.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110347"},"PeriodicalIF":0.9,"publicationDate":"2025-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143161020","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":"Universal distribution of the empirical coverage in split conformal prediction","authors":"Paulo C. Marques F.","doi":"10.1016/j.spl.2024.110350","DOIUrl":"10.1016/j.spl.2024.110350","url":null,"abstract":"<div><div>When split conformal prediction operates in batch mode with exchangeable data, we determine the exact distribution of the empirical coverage of prediction sets produced for a finite batch of future observables. This distribution is universal, being determined solely by the batch size, the nominal miscoverage level, and the calibration sample size. The exact distribution of the almost sure limit of the empirical coverage as the batch size goes to infinity is also identified, leading to a criterion for choosing the minimum required calibration sample size in applications.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110350"},"PeriodicalIF":0.9,"publicationDate":"2025-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143161017","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":"The stochastic MHD equations driven by pure jump noise in Lp spaces","authors":"Kaicheng Ni, Heling Su, Jiahui Zhu","doi":"10.1016/j.spl.2024.110351","DOIUrl":"10.1016/j.spl.2024.110351","url":null,"abstract":"<div><div>We consider the stochastic incompressible magnetohydrodynamic equations driven by additive jump noises on either the whole space <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>, <span><math><mrow><mi>d</mi><mo>=</mo><mn>2</mn><mo>,</mo><mn>3</mn></mrow></math></span> or a smooth bounded domain <span><math><mi>D</mi></math></span> in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>. We establish the local existence and uniqueness of a mild solution in the space <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msup><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>;</mo><msubsup><mrow><mi>L</mi></mrow><mrow><mi>σ</mi></mrow><mrow><mi>p</mi><mo>⊗</mo></mrow></msubsup><mrow><mo>(</mo><mi>D</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow></math></span> allowing for initial data with less regularity, including the marginal case <span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><msubsup><mrow><mi>L</mi></mrow><mrow><mi>σ</mi></mrow><mrow><mi>d</mi><mo>⊗</mo></mrow></msubsup><mrow><mo>(</mo><mi>D</mi><mo>)</mo></mrow></mrow></math></span>. In the two-dimensional case, we also prove the global existence of mild solutions.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110351"},"PeriodicalIF":0.9,"publicationDate":"2025-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143161018","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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