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Limit Properties of Record Numbers in Random walks

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arXiv 2024年

作者： Lu, Penghui Li, Yuqiang Yao, Qiang Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE School of Statistics East China Normal University Shanghai200062 China

In this paper, we systematically summarize and enhance the understanding of weak convergence and functional limits of record numbers in discrete-time random walks under Spitzer's condition, and extend these findings to σ-record numbers using similar methods. Additionally, we identify a sufficient condition for the existence of functional limits for record numbers in continuous-time random walks. Finally, we derive corresponding results for large deviations, moderate deviations, and laws of the iterated logarithm pertaining to record numbers in discrete-time random walks. Copyright © 2024, The Authors. All rights reserved.

关键词： Continuous time systems

Rejoinder on‘A review of distributed statistical inference’

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Statistical theory and Related Fields 2022年第2期6卷 111-113页

作者： Yuan Gao Weidong Liu Hansheng Wang Xiaozhou Wang Yibo Yana Riquan Zhang School of Statistics and Key Laboratory of Advanced Theory and Application in Statistics and Data Science–MOE East China Normal UniversityShanghaiPeople’s Republic of China School of Mathematical Sciences–School of Life Sciences and Biotechnology–MOE Key Lab of Artifcial Intelligence Shanghai Jiao Tong UniversityShanghaiPeople’s Republic of China Guanghua School of Management Peking UniversityBeijingPeople’s Republic of China

We thank the editor,Professor Jun Shao,for orga-nizing this stimulating *** are grateful to all discussants for their insightful comments on our review article on the distributed statistical *** to the urgent need to process the datasets with massive sizes,various distributed computing methods have been proposed for the large-scale statistical ***,some important theoretical results were *** we want to give a relatively comprehensive overview on this hot topic,there are still some important works that have been missed in our review written over a year ***,we are glad to see the discussants provide reviews of some new works and *** hope that these discussions and our review would serve as a stimulus for further studies in this rapidly developing area.

关键词： editor discussions sizes

Modelling Correlation Matrices in Multivariate Dyadic data: Latent Variable Models for Intergenerational Exchanges of Family Support

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arXiv 2022年

作者： Zhang, Siliang Kuha, Jouni Steele, Fiona Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE School of Statistics East China Normal University China Department of Statistics London School of Economics & Political Science United Kingdom

We define a model for the joint distribution of multiple continuous latent variables which includes a model for how their correlations depend on explanatory variables. This is motivated by and applied to social scientific research questions in the analysis of intergenerational help and support within families, where the correlations describe reciprocity of help between generations and complementarity of different kinds of help. We propose an MCMC procedure for estimating the model which maintains the positive definiteness of the implied correlation matrices, and describe theoretical results which justify this approach and facilitate efficient implementation of it. The model is applied to data from the UK Household Longitudinal Study to analyse exchanges of practical and financial support between adult individuals and their non-coresident parents. Copyright © 2022, The Authors. All rights reserved.

关键词： Covariance matrix

Regional consistency evaluation and sample size calculation under two MRCTs

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arXiv 2024年

作者： Qing, Kunhai Ren, Xinru Xu, Jin School of Statistics East China Normal University Shanghai China Key Laboratory of Advanced Theory and Application in Statistics and Data Science - MOE East China Normal University Shanghai China

Multi-regional clinical trial (MRCT) has been common practice for drug development and global registration. The FDA guidance "Demonstrating Substantial Evidence of Effectiveness for Human Drug and Biological Products Guidance for Industry" (FDA, 2019) requires that substantial evidence of effectiveness of a drug/biologic product to be demonstrated for market approval. In the situations where two pivotal MRCTs are needed to establish effectiveness of a specific indication for a drug or biological product, a systematic approach of consistency evaluation for regional effect is crucial. In this paper, we first present some existing regional consistency evaluations in a unified way that facilitates regional sample size calculation under the simple fixed effect model. Second, we extend the two commonly used consistency assessment criteria of MHLW (2007) in the context of two MRCTs and provide their evaluation and regional sample size calculation. Numerical studies demonstrate the proposed regional sample size attains the desired probability of showing regional consistency. A hypothetical example is provided for illustration of application. We provide an R package for implementation. Copyright © 2024, The Authors. All rights reserved.

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Large and moderate deviations for record numbers in some non–nearest neighbor random walks

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arXiv 2019年

作者： Li, Yuqiang Yao, Qiang Key Laboratory of Advanced Theory and Application in Statistics and Data Science–MOE School of Statistics East China Normal University China NYU–ECNU Institute of Mathematical Sciences NYU Shanghai China

The deviation principles of record numbers in random walk models have not been completely investigated, especially for the non–nearest neighbor cases. In this paper, we derive the asymptotic probabilities of large and moderate deviations for the number of "weak records" (or "ladder points") in two kinds of one–dimensional non–nearest neighbor random walks. The proofs depend only on the direct analysis of random walks. We illustrate that the traditional method of analyzing the local time of Brownian motions, which is often adopted for the simple random walks, would lead to wrong conjectures for our *** Codes 60F10, 60G50 Copyright © 2019, The Authors. All rights reserved.

关键词： Brownian movement

Confidence intervals and hypothesis testing for high-dimensional quantile regression: convolution smoothing and debiasing

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The Journal of Machine Learning Research

The Journal of Machine Learning Research 2023年第1期24卷 11626-11674页

作者： Yibo Yan Xiaozhou Wang Riquan Zhang School of Statistics East China Normal University Shanghai China School of Statistics Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE East China Normal University Shanghai China School of Statistics and Information Shanghai University of International Business and Economics Shanghai China

ℓ1-penalized quantile regression (ℓ1-QR) is a useful tool for modeling the relationship between input and output variables when detecting heterogeneous effects in the high-dimensional setting. Hypothesis tests can then be formulated based on the debiased ℓ1-QR estimator that reduces the bias induced by Lasso penalty. However, the nonsmoothness of the quantile loss brings great challenges to the computation, especially when the data dimension is high. Recently, the convolution-type smoothed quantile regression (SQR) model has been proposed to overcome such shortcoming, and people developed theory of estimation and variable selection therein. In this work, we combine the debiased method with SQR model and come up with the debiased ℓ1-SQR estimator, based on which we then establish confidence intervals and hypothesis testing in the high-dimensional setup. Theoretically, we provide the non-asymptotic Bahadur representation for our proposed estimator and also the Berry-Esseen bound, which implies the empirical coverage rates for the studentized confidence intervals. Furthermore, we build up the theory of hypothesis testing on both a single variable and a group of variables. Finally, we exhibit extensive numerical experiments on both simulated and real data to demonstrate the good performance of our method.

关键词： high-dimensional quantile regression convolution-based smoothing debiased method hypothesis testing non-asymptotic statistics

Search for lepton portal dark matter in the PandaX-4T experiment

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Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 2025年 864卷

作者： Ning, Xuyang Bo, Zihao Chen, Wei Chen, Xun Chen, Yunhua Cheng, Zhaokan Cui, Xiangyi Fan, Yingjie Fang, Deqing Gao, Zhixing Geng, Lisheng Giboni, Karl Guo, Xunan Guo, Xuyuan Guo, Zichao Han, Chencheng Han, Ke He, Changda He, Jinrong Huang, Di Huang, Houqi Huang, Junting Hou, Ruquan Hou, Yu Ji, Xiangdong Ji, Xiangpan Ju, Yonglin Li, Chenxiang Li, Jiafu Li, Mingchuan Li, Shuaijie Li, Tao Li, Zhiyuan Lin, Qing Liu, Jianglai Lu, Congcong Lu, Xiaoying Luo, Lingyin Luo, Yunyang Ma, Wenbo Ma, Yugang Mao, Yajun Meng, Yue Pang, Binyu Qi, Ningchun Qian, Zhicheng Ren, Xiangxiang Shan, Dong Shang, Xiaofeng Shao, Xiyuan Shen, Guofang Shen, Manbin Sun, Wenliang Tao, Yi Wang, Anqing Wang, Guanbo Wang, Hao Wang, Jiamin Wang, Lei Wang, Meng Wang, Qiuhong Wang, Shaobo Wang, Siguang Wang, Wei Wang, Xiuli Wang, Xu Wang, Zhou Wei, Yuehuan Wu, Weihao Wu, Yuan Xiao, Mengjiao Xiao, Xiang Xiong, Kaizhi Xu, Yifan Yao, Shunyu Yan, Binbin Yan, Xiyu Yang, Yong Ye, Peihua Yu, Chunxu Yuan, Ying Yuan, Zhe Yun, Youhui Zeng, Xinning Zhang, Minzhen Zhang, Peng Zhang, Shibo Zhang, Shu Zhang, Tao Zhang, Wei Zhang, Yang Zhang, Yingxin Zhang, Yuanyuan Zhao, Li Zhou, Jifang Zhou, Jiaxu Zhou, Jiayi Zhou, Ning Zhou, Xiaopeng Zhou, Yubo Zhou, Zhizhen Bai, Yang Tsung-Dao Lee Institute Shanghai Jiao Tong University Shanghai 201210 China School of Physics and Astronomy Shanghai Jiao Tong University Shanghai 200240 China State Key Laboratory of Dark Matter Physics Key Laboratory for Particle Astrophysics and Cosmology (MoE) Shanghai Key Laboratory for Particle Physics and Cosmology New Cornerstone Science Laboratory Shanghai Jiao Tong University Shanghai 200240 China Shanghai Jiao Tong University Sichuan Research Institute Chengdu 610213 China Jinping Deep Underground Frontier Science and Dark Matter Key Laboratory of Sichuan Province Liangshan 615000 China Yalong River Hydropower Development Company Ltd. 288 Shuanglin Road Chengdu 610051 China Sino-French Institute of Nuclear Engineering and Technology Sun Yat-Sen University Zhuhai 519082 China Department of Physics Yantai University Yantai 264005 China Key Laboratory of Nuclear Physics Ion-beam Application (MOE) Institute of Modern Physics Fudan University Shanghai 200433 China School of Physics Beihang University Beijing 102206 China Peng Huanwu Collaborative Center for Research and Education Beihang University Beijing 100191 China International Research Center for Nuclei and Particles in the Cosmos Beijing Key Laboratory of Advanced Nuclear Materials and Physics Beihang University Beijing 100191 China Southern Center for Nuclear-Science Theory (SCNT) Institute of Modern Physics Chinese Academy of Sciences Huizhou 516000 China SJTU Paris Elite Institute of Technology Shanghai Jiao Tong University Shanghai 200240 China School of Mechanical Engineering Shanghai Jiao Tong University Shanghai 200240 China Department of Physics University of Maryland College Park 20742 MD United States School of Physics Nankai University Tianjin 300071 China School of Physics Sun Yat-Sen University Guangzhou 510275 China State Key Laboratory of Particle Detection and Electronics University of Science and Technology of China Hefei 230026 China Department of Mod

We report a search for a lepton-portal dark matter model, where dark matter couples to a charged lepton in the standard model. This simplified model naturally leads to photon-mediated dark matter interactions with nuclei, making it suitable for direct dark matter detection experiments. Matching to the framework of non-relativistic effective field theory for dark matter, we report the first sensitive search for this model using data from the PandaX-4T commissioning run. Our results yield strong constraints on Dirac fermion dark matter but relatively weaker constraints on Majorana dark matter due to the suppression of effective photon interactions. These constraints complement those obtained from the collider and indirect detection experiments. © 2025 The Author(s)

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Spatially Clustered Varying Coefficient Model

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arXiv 2020年

作者： Lin, Fangzheng Tang, Yanlin Zhu, Huichen Zhu, Zhongyi Department of Statistics Fudan University China Key Laboratory of Advanced Theory and Application in Statistics and Data Science - MOE School of Statistics East China Normal University China Department of Mathematics Hong Kong University of Science and Technology China

In various applications with large spatial regions, the relationship between the response variable and the covariates is expected to exhibit complex spatial patterns. We propose a spatially clustered varying coefficient model, where the regression coefficients are allowed to vary smoothly within each cluster but change abruptly across the boundaries of adjacent clusters, and we develop a unified approach for simultaneous coefficient estimation and cluster identification. The varying coefficients are approximated by penalized splines, and the clusters are identified through a fused concave penalty on differences in neighboring locations, where the spatial neighbors are specified by the minimum spanning tree (MST). The optimization is solved efficiently based on the alternating direction method of multipliers, utilizing the sparsity structure from MST. Furthermore, we establish the oracle property of the proposed method considering the structure of MST. Numerical studies show that the proposed method can efficiently incorporate spatial neighborhood information and automatically detect possible spatially clustered patterns in the regression coefficients. An empirical study in oceanography illustrates that the proposed method is promising to provide informative results. Copyright © 2020, The Authors. All rights reserved.

关键词： Constrained optimization

Causal Mediation Analysis with a Three-Dimensional Image Mediator

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arXiv 2023年

作者： Chen, Minghao Zhou, Yingchun Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE Institute of Brain and Education Innovation School of Statistics East China Normal University 3663 North Zhongshan Road Shanghai200062 China

Causal mediation analysis is increasingly abundant in biology, psychology, and epidemiology studies, etc. In particular, with the advent of the big data era, the issue of high-dimensional mediators is becoming more prevalent. In neuroscience, with the widespread application of magnetic resonance technology in the field of brain imaging, studies on image being a mediator emerged. In this study, a novel causal mediation analysis method with a three-dimensional image mediator is proposed. We define the average casual effects under the potential outcome framework, explore several sufficient conditions for the valid identification, and develop techniques for estimation and inference. To verify the effectiveness of the proposed method, a series of simulations under various scenarios is performed. Finally, the proposed method is applied to a study on the causal effect of mother's delivery mode on child's IQ development. It is found that the white matter in certain regions of the frontal-parietal and brainstem-cerebellum areas has mediating effects. © 2023, CC BY.

关键词： Magnetic resonance