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A class of admissible estimators of multiple regression coefficient with an unknown variance

Statistical theory and Related Fields 2020年第2期4卷 190-201页

作者： Chengyuan Song Dongchu Sun Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE School of StatisticsEast China Normal UniversityShanghaiPeople’s Republic of China Department of Statistics University of Nebraska-LincolnLincolnNEUSA

Suppose that we observe y|θ,τ∼N_(p)(Xθ,τ^(−1)I_(p)),where θ is an unknown vector with unknown precisionτ.Estimating the regression coefficient θ with known τ has been well ***,statistical properties such as admissibility in estimating θ with unknownτare not well ***[(2009).Topics in shrinkage estimation and in causal inference(PhD thesis).Warton School,University of Pennsylvania]appears to be the first to consider the problem,developing sufficient conditions for the admissibility of estimating means of multivariate normal distributions with unknown *** generalise the sufficient conditions for admissibility and apply these results to the normal linear regression model.2-level and 3-level hierarchical models with unknown precisionτare investigated when a standard class of hierarchical priors leads to admissible estimators of θ under the normalised squared error *** reason to consider this problem is the importance of admissibility in the hierarchical prior selection,and we expect that our study could be helpful in providing some reference for choosing hierarchical priors.

关键词： Admissible estimators unknown variance multivariate normal distributions hierarchical models

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The kth Power Expectile Estimation and Testing

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Communications in Mathematics and statistics 2024年第4期12卷 573-615页

作者： Fuming Lin Yingying Jiang Yong Zhou College of Mathematics and Statistics Sichuan University of Science and EngineeringZigongSichuanPeople’s Republic of China South Sichuan Center for Applied Mathematics ZigongSichuanPeople’s Republic of China Key Laboratory of Advanced Theory and Application in Statistics and Data Science MOEand Academy of Statistics and Interdisciplinary Sciences and School of StatisticsEast China Normal UniversityShanghaiPeople’s Republic of China

This paper develops the theory of the kth power expectile estimation and considers its relevant hypothesis tests for coefficients of linear regression *** prove that the asymptotic covariance matrix of kth power expectile regression converges to that of quantile regression as k converges to one and hence promise a moment estimator of asymptotic matrix of quantile *** kth power expectile regression is then utilized to test for homoskedasticity and conditional symmetry of the *** comparisons of the local power among the kth power expectile regression tests,the quantile regression test,and the expectile regression test have been *** the underlying distribution is not standard normal,results show that the optimal k are often larger than 1 and smaller than 2,which suggests the general kth power expectile regression is ***,the methods are illustrated by a real example.

关键词： The kth power expectiles Expectiles Quantiles Testing for homoskedasticity Testing for conditional symmetry Estimating asymptotic matrix of quantile regression

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Research on a quantification model of online learning cognitive load based on eye-tracking technology

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Multimedia Tools and applications 2024年 1-15页

作者： Xue, Yaofeng Zhu, Fangqing Li, Jiaxuan Department of Educational Information Technology and Shanghai Engineering Research Center of Digital Educational Equipment East China Normal University Shanghai200062 China Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE East China Normal University Shanghai China

Online learning is characterized by a high degree of complexity and a wealth of information when compared to traditional classroom learning. This can have an adverse influence on the learning outcomes of online learners. The paper builds a quantification model of online learning cognitive load based on non-invasive eye-tracking technology by combining three eye-movement indicators: fixation time, fixation count, and pupil diameter. This is based on the analysis of cognitive load and eye-tracking technology. The study then uses a significant amount of eye movement experimental data in conjunction with the cognitive load test that students take in an online learning environment to confirm the viability and effectiveness of the quantification methodology. The paper builds a quantification model of online learning cognitive load based on non-invasive eye-tracking technology by combining three eye-movement indicators: fixation time, fixation count, and pupil diameter. This is based on the analysis of cognitive load and eye-tracking technology. The study then uses a significant amount of eye movement experimental data in conjunction with the cognitive load test that students take in an online learning environment to confirm the viability and effectiveness of the quantification methodology. © The Author(s), under exclusive licence to Springer science+Business Media, LLC, part of Springer Nature 2024.

关键词： Eye movements

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Exponential tilted likelihood for stationary time series models

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Statistical theory and Related Fields 2022年第3期6卷 254-263页

作者： Xiuzhen Zhang Yukun Liu Riquan Zhang Zhiping Lu Key Laboratory of Advanced Theory and Application in Statistics and Data Science MOESchool of StatisticsEast China Normal UniversityShanghaiPeople’s Republic of China School of Mathematics and Statistics Shanxi Datong UniversityDatongPeople’s Republic of China

Depending on the asymptotical independence of periodograms,exponential tilted(ET)likelihood,as an effective nonparametric statistical method,is developed to deal with time series in this *** to empirical likelihood(EL),it still suffers from two drawbacks:the nondefinition problem of the likelihood function and the under-coverage probability of confidence *** overcome these two problems,we further proposed the adjusted ET(AET)*** a specific adjustment level,our simulation studies indicate that the AET method achieves a higher-order coverage precision than the unadjusted ET *** addition,due to the good performance of ET under moment model misspecification[Schennach,S.M.(2007).Point estimation with exponentially tilted empirical *** Annals of statistics,35(2),634–***://***/10.1214/009053606000001208],we show that the one-order property of point estimate is preserved for the misspecified spectral estimating equations of the autoregressive coefficient of AR(1).The simulation results illustrate that the point estimates of the ET outperform those of the EL and their hybrid in terms of standard deviation.A real data set is analyzed for illustration purpose.

关键词： Exponential tilted likelihood adjusted exponential tilted likelihood stationary time series misspecified moment model

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A GMM approach in coupling internal data and external summary information with heterogeneous data populations

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science China Mathematics 2024年第5期67卷 1115-1132页

作者： Jun Shao Jinyi Wang Lei Wang Key Laboratory of Advanced Theory and Application in Statistics and Data Science(East China Normal University) Ministry of EducationShanghai 200062China School of Statistics East China Normal UniversityShanghai 200062China Department of Statistics University of Wisconsin-MadisonWI 53706USA School of Statistics and Data Science KLMDASRLEBPS and LPMCNankai UniversityTianjin 300071China

Because of advances in data collection and storage,statistical analysis in modern scientific research and practice now has opportunities to utilize external information such as summary statistics from similar studies.A likelihood approach based on a parametric model assumption has been developed in the literature to utilize external summary information when the populations for external and main internal data are assumed to be the *** this article,we instead consider the generalized estimation equation(GEE)approach for statistical inference,which is semiparametric or nonparametric,and show how to utilize external summary information even when internal and external data populations are not the *** approach is coupling the internal data and external summary information to form additional estimation equations and then applying the generalized method of moments(GMM).We show that the proposed GMM estimator is asymptotically normal and,under some conditions,is more efficient than the GEE estimator without using external summary *** of the asymptotic covariance matrix of the GMM estimators are also *** results are obtained to confirm our theory and quantify the improvements by utilizing external *** example is also included for illustration.

关键词： adjustment for heterogeneity constraint data integration generalized method of moments summarystatistic

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Semiparametric estimation for accelerated failure time mixture cure model allowing non-curable competing risk

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Statistical theory and Related Fields 2020年第1期4卷 97-108页

作者： Yijun Wang Jiajia Zhang Yincai Tang Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE School of StatisticsEast China Normal UniversityShanghai200062People’s Republic of China Department of Epidemiology and Biostatistics University of South CarolinaColumbiaSCUSA

The mixture cure model is the most popular model used to analyse the major event with a potential cure *** in the real world there may exist a potential risk from other non-curable competing *** this paper,we study the accelerated failure time model with mixture cure model via kernel-based nonparametric maximum likelihood estimation allowing non-curable competing *** EM algorithm is developed to calculate the estimates for both the regression parameters and the unknown error densities,in which a kernel-smoothed conditional profile likelihood is maximised in the M-step,and the resulting estimates are *** performance is demonstrated through comprehensive simulation ***,the proposed method is applied to the colorectal clinical trial data.

关键词： AFT mixture cure model competing risk EM algorithm

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A Double Varying-coefficient Modeling Approach for Analyzing Longitudinal Observations

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Acta Mathematicae Applicatae Sinica 2019年第3期35卷 671-688页

作者： Qun-fang XU Rui LI School of Business Ningbo UniversityNingbo 315211China School of Statistics and Information Shanghai University of International Business and EconomicsShanghai 201620China Key Laboratory of Advanced Theory and Application in Statistics and Data Science East China Normal UniversityMinistry of EducationShanghai 200062China

The identification of within-subject dependence is important for constructing efficient estimation in longitudinal data *** this paper,we proposed a flexible way to study this dependence by using nonparametric regression ***,we considered the estimation of varying coefficient longitudinal data model with non-stationary varying coefficient autoregressive error process over observational time *** on spline approximation and local polynomial techniques,we proposed a two-stage nonparametric estimation for unknown functional coefficients and didn’t not drop any observations in a hybrid least square loss ***,we showed that the estimated coefficient functions are asymptotically normal and derived the asymptotic biases and variances *** Carlo studies and two real applications were conducted for illustrating the performance of our proposed methods.

关键词： autoregressive process double varying coefficient irregular time quantum locally linear

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The abstract of doctoral dissertation‘nonlinear wavelet density estimation and hazard rate estimation with data missing at random’

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Statistical theory and Related Fields 2020年第1期4卷 117-119页

作者： Yuye Zou Guoliang Fan Riquan Zhang School of Economics and Management Shanghai Maritime UniversityShanghaiPeople’s Republic of China Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE School of StatisticsEast China Normal UniversityShanghaiPeople’s Republic of China

In this thesis,we establish non-linear wavelet density estimators and studying the asymptotic properties of the estimators with data missing at random when covariates are *** outstanding advantage of non-linear wavelet method is estimating the unsoothed functions,however,the classical kernel estimation cannot do this *** the same time,we study the larger sample properties of the ISE for hazard rate estimator.

关键词： Asymptotic normality integral square error mean integral square error missing at random non-linear wavelet

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Search for Solar Boosted Dark Matter Particles at the PandaX-4T Experiment

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Physical Review Letters 2025年第16期134卷 161003-161003页

作者： Guofang Shen Zihao Bo Wei Chen Xun Chen Yunhua Chen Zhaokan Cheng Xiangyi Cui Yingjie Fan Deqing Fang Zhixing Gao Lisheng Geng Karl Giboni Xunan Guo Xuyuan Guo Zichao Guo Chencheng Han Ke Han Changda He Jinrong He Di Huang Houqi Huang Junting Huang Ruquan Hou Yu Hou Xiangdong Ji Xiangpan Ji Yonglin Ju Chenxiang Li Jiafu Li Mingchuan Li Shuaijie Li Tao Li Zhiyuan Li Qing Lin Jianglai Liu Congcong Lu Xiaoying Lu Lingyin Luo Yunyang Luo Wenbo Ma Yugang Ma Yajun Mao Yue Meng Xuyang Ning Binyu Pang Ningchun Qi Zhicheng Qian Xiangxiang Ren Dong Shan Xiaofeng Shang Xiyuan Shao Manbin Shen Wenliang Sun Yi Tao 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 Wang Yuehuan Wei Weihao Wu Yuan Wu Mengjiao Xiao Xiang Xiao Kaizhi Xiong Yifan Xu Shunyu Yao Binbin Yan Xiyu Yan Yong Yang Peihua Ye Chunxu Yu Ying Yuan Zhe Yuan Youhui Yun Xinning Zeng Minzhen Zhang Peng Zhang Shibo Zhang Shu Zhang Tao Zhang Wei Zhang Yang Zhang Yingxin Zhang Yuanyuan Zhang Li Zhao Jifang Zhou Jiaxu Zhou Jiayi Zhou Ning Zhou Xiaopeng Zhou Yubo Zhou Zhizhen Zhou Haipeng An Haoming Nie School of Physics Beihang University Beijing 102206 China School of Physics and Astronomy Shanghai Jiao Tong University Key Laboratory for Particle Astrophysics and Cosmology (MoE) Shanghai Key Laboratory for Particle Physics and Cosmology Shanghai 200240 China New Cornerstone Science Laboratory Tsung-Dao Lee Institute Shanghai Jiao Tong University Shanghai 201210 China Shanghai Jiao Tong University Sichuan Research Institute Chengdu 610213 China Jinping Deep Underground Frontier Science and Dark Matter Key Laboratory of Sichuan Province 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 and Ion-beam Application (MoE) Institute of Modern Physics Fudan University Shanghai 200433 China Peng Huanwu Collaborative Center for Research and Education Beihang University Beijing 100191 China International Research Center for Nuclei and Particles in the Cosmos and 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 Maryland 20742 USA 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 Modern Physics University of Science and Technology of China Hefei 230026 China Research Center for Particle Science and Technology

We present a novel constraint on light dark matter utilizing 1.54 metric ton/year of data acquired from the PandaX-4T dual-phase xenon time projection chamber. This constraint is derived through detecting electronic recoil signals resulting from the interaction with solar-enhanced dark matter flux. Low-mass dark matter particles, lighter than a few MeV/c2, can scatter with the thermal electrons in the Sun. Consequently, with higher kinetic energy, the boosted dark matter component becomes detectable via contact scattering with xenon electrons, resulting in a few keV energy deposition that exceeds the threshold of PandaX-4T. We calculate the expected recoil energy in PandaX-4T considering the Sun’s acceleration with heavy mediators and the detection capabilities of the xenon detector. The first experimental search results using the xenon detector yield the most stringent upper limits cross section of 3.51×10−39 cm2 at 0.08 MeV/c2 for a solar boosted dark matter mass ranging from 0.02 to 10 MeV/c2, achieving a 23-fold improvement compared with earlier experimental studies.

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Weighted Euclidean balancing for a matrix exposure in estimating causal effect

arXiv

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arXiv 2023年

作者： Chen, Juan Zhou, Yingchun Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE School of Statistics East China Normal China

In many scientific fields such as biology, psychology and sociology, there is an increasing interest in estimating the causal effect of a matrix exposure on an outcome. Covariate balancing is crucial in causal inference and both exact balancing and approximate balancing methods have been proposed in the past decades. However, due to the large number of constraints, it is difficult to achieve exact balance or to select the threshold parameters for approximate balancing methods when the treatment is a matrix. To meet these challenges, we propose the weighted Euclidean balancing method, which approximately balance covariates from an overall perspective. This method is also applicable to high-dimensional covariates scenario. Both parametric and nonparametric methods are proposed to estimate the causal effect of matrix treatment and theoretical properties of the two estimations are provided. Furthermore, the simulation results show that the proposed method outperforms other methods in various cases. Finally, the method is applied to investigating the causal relationship between children's participation in various training courses and their IQ. The results show that the duration of attending hands-on practice courses for children at 6-9 years old has a siginificantly positive impact on children's IQ. © 2023, CC BY.

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