{"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}
{"title":"A general type of weak comparison theorems for BDSDEs","authors":"Jinghan Wang , Yufeng Shi , Nana Zhao","doi":"10.1016/j.spl.2024.110353","DOIUrl":"10.1016/j.spl.2024.110353","url":null,"abstract":"<div><div>In this paper we study a special type of weak comparison theorems for backward doubly stochastic differential equations (BDSDEs, in short). It is worth emphasizing that, unlike the comparison theorems in the previous literature, which all require that the coefficients <span><math><mrow><msup><mrow><mi>g</mi></mrow><mrow><mrow><mo>(</mo><mi>i</mi><mo>)</mo></mrow></mrow></msup><mo>,</mo><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></math></span> of the doubly stochastic integration term must be same, we allow the coefficients <span><math><mrow><msup><mrow><mi>g</mi></mrow><mrow><mrow><mo>(</mo><mi>i</mi><mo>)</mo></mrow></mrow></msup><mo>,</mo><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></math></span> to be different in this paper. In addition, we extend this conclusion to a class of general mean-field backward doubly stochastic differential equations (mean-field BDSDEs, in short), in which the coefficient <span><math><mi>f</mi></math></span> not only depends on the solution processes <span><math><mrow><mi>y</mi><mo>,</mo><mi>z</mi></mrow></math></span>, but also depends on the law of the solution, i.e. <span><math><mi>μ</mi></math></span>, which describes the characteristic of the mean-field.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110353"},"PeriodicalIF":0.9,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143161521","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":"Functional-coefficient quantile cointegrating regression with stationary covariates","authors":"Haiqi Li , Jing Zhang , Chaowen Zheng","doi":"10.1016/j.spl.2024.110344","DOIUrl":"10.1016/j.spl.2024.110344","url":null,"abstract":"<div><div>This study examines the estimation and inference of functional-coefficient quantile cointegrating regression. Firstly, a local linear quantile regression estimator is proposed to estimate the unknown coefficient function. Secondly, to alleviate the endogeneity problem, we propose a nonparametric fully-modified quantile regression estimator that is shown to be <span><math><mrow><mi>n</mi><msqrt><mrow><mi>h</mi></mrow></msqrt></mrow></math></span> consistent and follow a mixed normal distribution asymptotically. Thirdly, we propose two Kolmogorov–Smirnov type test statistics for coefficient stability in a given quantile or across multiple quantile levels. Finally, to improve the finite sample performance, we propose a fixed regressor wild bootstrap procedure and establish its asymptotic validity. Monte Carlo simulation results confirm the merits of the proposed estimator and tests.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110344"},"PeriodicalIF":0.9,"publicationDate":"2024-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143161022","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":"Explicit bounds for a Gaussian decomposition Lemma of Sellke","authors":"Tobias Schmidt","doi":"10.1016/j.spl.2024.110342","DOIUrl":"10.1016/j.spl.2024.110342","url":null,"abstract":"<div><div>In <span><span>Sellke (2024)</span></span> a decomposition of Gaussian measures on finite dimensional spaces was introduced, which turned out to be a central technical tool to improve currently known bounds on a long standing conjecture in statistical mechanics called the Polaron problem. This note slightly generalizes this decomposition and provides numerical values for all occurring constants.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110342"},"PeriodicalIF":0.9,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143161015","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":"Two-barriers-reflected BSDE with rank-based data","authors":"Xinwei Feng, Lu Wang","doi":"10.1016/j.spl.2024.110343","DOIUrl":"10.1016/j.spl.2024.110343","url":null,"abstract":"<div><div>We investigate two-barriers-reflected backward stochastic differential equations with data from rank-based stochastic differential equation. More specifically, we focus on the solution of backward stochastic differential equations restricted to two prescribed upper-boundary and lower-boundary processes. We rigorously show that this solution gives a probabilistic expression to the viscosity solution of some obstacle problems for the corresponding parabolic partial differential equations. As an application, the pricing problem of an American game option is studied.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110343"},"PeriodicalIF":0.9,"publicationDate":"2024-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143161019","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 law of the iterated logarithm for functionals of the Wiener process","authors":"A. Logachov , A. Yambartsev","doi":"10.1016/j.spl.2024.110341","DOIUrl":"10.1016/j.spl.2024.110341","url":null,"abstract":"<div><div>In this note, we establish a law of the iterated logarithm for Fréchet differentiable functionals of a general form with respect to the Wiener process for a small time. The proof method shares conceptual similarities with the delta method.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"219 ","pages":"Article 110341"},"PeriodicalIF":0.9,"publicationDate":"2024-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143161023","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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