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Comparing time varying regression quantiles under shift invariance 移位不变性下时变回归分位数的比较
IF 1.5 2区 数学
Bernoulli Pub Date : 2023-05-01 DOI: 10.3150/22-bej1509
S. S. Dhar, Weichi Wu
{"title":"Comparing time varying regression quantiles under shift invariance","authors":"S. S. Dhar, Weichi Wu","doi":"10.3150/22-bej1509","DOIUrl":"https://doi.org/10.3150/22-bej1509","url":null,"abstract":"This article investigates whether time-varying quantile regression curves are the same up to the horizontal shift or not. The errors and the covariates involved in the regression model are allowed to be locally stationary. We formalize this issue in a corresponding non-parametric hypothesis testing problem, and develop an integrated-squared-norm based test (SIT) as well as a simultaneous confidence band (SCB) approach. The asymptotic properties of SIT and SCB under null and local alternatives are derived. Moreover, the asymptotic properties of these tests are also studied when the compared data sets are dependent. We then propose valid wild bootstrap algorithms to implement SIT and SCB. Furthermore, the usefulness of the proposed methodology is illustrated via analysing simulated and real data related to COVID-19 outbreak and climate science. bootstrap, comparison of curves, confidence band, hypothesis testing, locally stationary process, nonparametric quantile regression, COVID-19. 1 ar X iv :2 01 1. 06 33 3v 2 [ st at .M E ] 2 4 D ec 2 02 1","PeriodicalId":55387,"journal":{"name":"Bernoulli","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46907323","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Combinatorial Bernoulli factories 组合伯努利工厂
IF 1.5 2区 数学
Bernoulli Pub Date : 2023-05-01 DOI: 10.3150/22-bej1497
Rad Niazadeh, Renato Paes Leme, Jon Schneider
{"title":"Combinatorial Bernoulli factories","authors":"Rad Niazadeh, Renato Paes Leme, Jon Schneider","doi":"10.3150/22-bej1497","DOIUrl":"https://doi.org/10.3150/22-bej1497","url":null,"abstract":"","PeriodicalId":55387,"journal":{"name":"Bernoulli","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41810507","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Fisher’s measure of variability in repeated samples 重复样本变异性的Fisher测度
IF 1.5 2区 数学
Bernoulli Pub Date : 2023-05-01 DOI: 10.3150/22-bej1494
Poly H. da Silva, Arash Jamshidpey, P. McCullagh, S. Tavaré
{"title":"Fisher’s measure of variability in repeated samples","authors":"Poly H. da Silva, Arash Jamshidpey, P. McCullagh, S. Tavaré","doi":"10.3150/22-bej1494","DOIUrl":"https://doi.org/10.3150/22-bej1494","url":null,"abstract":"Fisher (1943) claimed that the expected value of the sample variance of the number of species found in large samples, each of n specimens taken from the same population, is asymptotically θ log2. This is at odds with the value θ log n obtained directly from the Ewens Sampling Formula (ESF), where θ specifies the rate at which new species are found. To resolve this apparent contradiction, we assume the species frequency spectrum in the population is determined by the ESF and that the samples are disjoint subsets drawn sequentially from this single population. We find an explicit formula for the required expected value for p samples of arbitrary size; in the limit of large equally-sized samples, it indeed has the value θ log2. We obtain limit theorems for the sample variance of p samples of size n under various limiting regimes as p , n or both tend to ∞ . We discuss further the behavior of the number of species present in all samples, and revisit Fisher’s log-series distribution as the limiting distribution of the number of specimens observed in typical species in a future, large sample.","PeriodicalId":55387,"journal":{"name":"Bernoulli","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47259624","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Central limit theorem of linear spectral statistics of high-dimensional sample correlation matrices 高维样本相关矩阵线性谱统计的中心极限定理
IF 1.5 2区 数学
Bernoulli Pub Date : 2023-05-01 DOI: 10.3150/22-bej1487
Yanqing Yin, Shu-rong Zheng, Tingting Zou
{"title":"Central limit theorem of linear spectral statistics of high-dimensional sample correlation matrices","authors":"Yanqing Yin, Shu-rong Zheng, Tingting Zou","doi":"10.3150/22-bej1487","DOIUrl":"https://doi.org/10.3150/22-bej1487","url":null,"abstract":"A high-dimensional sample correlation matrix is an important random matrix in multivariate statistical analysis. Its central limit theory is one of the main theoretical bases for making statistical inferences on high-dimensional correlation matrices. Under the high-dimensional framework in which the data dimension tends to infinity proportionally with the sample size, we establish the central limit theorems (CLT) for the linear spectral statistics (LSS) of sample correlation matrices in two settings: (1) the population follows an independent component structure; (2) the population follows an elliptical structure, including some heavy-tailed distributions. The results show that the CLTs of the LSS of the sample correlation matrices are very different in the two settings. In particular, even if the population correlation matrix is an identity matrix, the CLTs are different in the two settings. An application of our two established CLTs is provided.","PeriodicalId":55387,"journal":{"name":"Bernoulli","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44450673","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Convergence of the one-dimensional contact process with two types of particles and priority 两类粒子一维接触过程的收敛性和优先性
IF 1.5 2区 数学
Bernoulli Pub Date : 2023-05-01 DOI: 10.3150/22-bej1501
Mariela Pentón Machado
{"title":"Convergence of the one-dimensional contact process with two types of particles and priority","authors":"Mariela Pentón Machado","doi":"10.3150/22-bej1501","DOIUrl":"https://doi.org/10.3150/22-bej1501","url":null,"abstract":"","PeriodicalId":55387,"journal":{"name":"Bernoulli","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41271653","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Poisson approximation in χ2 distance by the Stein-Chen approach 用Stein-Chen方法在χ2距离上的泊松近似
IF 1.5 2区 数学
Bernoulli Pub Date : 2023-05-01 DOI: 10.3150/22-bej1512
V. Zacharovas
{"title":"Poisson approximation in χ2 distance by the Stein-Chen approach","authors":"V. Zacharovas","doi":"10.3150/22-bej1512","DOIUrl":"https://doi.org/10.3150/22-bej1512","url":null,"abstract":"","PeriodicalId":55387,"journal":{"name":"Bernoulli","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45736863","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A note on one-dimensional Poincaré inequalities by Stein-type integration 关于一维庞卡罗不等式的斯坦型积分注记
IF 1.5 2区 数学
Bernoulli Pub Date : 2023-05-01 DOI: 10.3150/22-bej1518
Gilles Germain, Yvik Swan
{"title":"A note on one-dimensional Poincaré inequalities by Stein-type integration","authors":"Gilles Germain, Yvik Swan","doi":"10.3150/22-bej1518","DOIUrl":"https://doi.org/10.3150/22-bej1518","url":null,"abstract":"","PeriodicalId":55387,"journal":{"name":"Bernoulli","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45509497","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Nonstationary fractionally integrated functional time series 非平稳分数积分函数时间序列
IF 1.5 2区 数学
Bernoulli Pub Date : 2023-05-01 DOI: 10.3150/22-bej1508
Degui Li, P. Robinson, H. Shang
{"title":"Nonstationary fractionally integrated functional time series","authors":"Degui Li, P. Robinson, H. Shang","doi":"10.3150/22-bej1508","DOIUrl":"https://doi.org/10.3150/22-bej1508","url":null,"abstract":"","PeriodicalId":55387,"journal":{"name":"Bernoulli","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46194458","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 12
General construction and classes of explicit L1-optimal couplings 显式l1 -最优耦合的一般构造和分类
2区 数学
Bernoulli Pub Date : 2023-02-01 DOI: 10.3150/22-bej1481
Giovanni Puccetti, Ludger Rüschendorf
{"title":"General construction and classes of explicit L1-optimal couplings","authors":"Giovanni Puccetti, Ludger Rüschendorf","doi":"10.3150/22-bej1481","DOIUrl":"https://doi.org/10.3150/22-bej1481","url":null,"abstract":"The main scope of this paper is to give some explicit classes of examples of L1-optimal couplings. Optimal transportation w.r.t. the Kantorovich metric ℓ1 (resp. the Wasserstein metric W1) between two absolutely continuous measures is known since the basic papers of Kantorovich and Rubinstein (Dokl. Akad. Nauk SSSR 115 (1957) 1058–1061) and Sudakov (Proc. Steklov Inst. Math. 141 (1979) 1–178) to occur on rays induced by a decomposition of the basic space (and more generally to higher dimensional decompositions in the case of general measures) induced by the corresponding dual potentials. Several papers have given this kind of structural result and established existence and uniqueness of solutions in varying generality. Since the dual problems pose typically too strong challenges to be solved in explicit form, these structural results have so far been applied for the solution of few particular instances. First, we give a self-contained review of some basic optimal coupling results and we propose and investigate in particular some basic principles for the construction of L1-optimal couplings given by a reduction principle and some usable forms of the decomposition method. This reduction principle, together with symmetry properties of the reduced measures, gives a hint to the decomposition of the space into sectors and via the non crossing property of optimal transport leads to the choice of transportation rays. The optimality of the induced transports is then a consequence of the characterization results of optimal couplings. Then, we apply these principles to determine in explicit form L1-optimal couplings for several classes of examples of elliptical distributions. In particular, we give for the first time a general construction of L1-optimal couplings between two bivariate Gaussian distributions. We also discuss optimality of special constructions like shifts and scalings, and provide an extended class of dual functionals allowing for the closed-form computation of the ℓ1-metric or of accurate lower bounds of it in a variety of examples.","PeriodicalId":55387,"journal":{"name":"Bernoulli","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136062377","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Variational formulas for asymptotic variance of general discrete-time Markov chains 一般离散马尔可夫链渐近方差的变分公式
2区 数学
Bernoulli Pub Date : 2023-02-01 DOI: 10.3150/21-bej1458
Lu-Jing Huang, Yong-Hua Mao
{"title":"Variational formulas for asymptotic variance of general discrete-time Markov chains","authors":"Lu-Jing Huang, Yong-Hua Mao","doi":"10.3150/21-bej1458","DOIUrl":"https://doi.org/10.3150/21-bej1458","url":null,"abstract":"The asymptotic variance is an important criterion to evaluate the performance of Markov chains, especially for the central limit theorems. We give the variational formulas for the asymptotic variance of discrete-time (non-reversible) Markov chains on general state space. The variational formulas provide many applications, extending the classical Peskun’s comparison theorem to non-reversible Markov chains, and obtaining several comparison theorems between Markov chains with various perturbations.","PeriodicalId":55387,"journal":{"name":"Bernoulli","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136062378","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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