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Variable screening in multivariate linear regression with high-dimensional covariates

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Statistical theory and Related Fields 2022年第3期6卷 241-253页

作者： Shiferaw B.Bizuayehu Lu Li Jin Xu School of Statistics East China Normal UniversityShanghaiPeople’s Republic of China School of Mathematical Sciences Shanghai Jiao Tong UniversityShanghaiPeople’s Republic of China Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE East China Normal UniversityShanghaiPeople’s Republic of China

We propose two variable selection methods in multivariate linear regression with highdimensional *** first method uses a multiple correlation coefficient to fast reduce the dimension of the relevant predictors to a moderate or low *** second method extends the univariate forward regression of Wang[(2009).Forward regression for ultra-high dimensional variable *** of the American Statistical Association,104(488),1512–***://***/10.1198/***08516]in a unified way such that the variable selection and model estimation can be obtained *** establish the sure screening property for both *** and real data applications are presented to show the finite sample performance of the proposed methods in comparison with some naive method.

关键词： Dimension reduction forward regression multiple correlation coefficient multivariate regression variable selection

A review of distributed statistical inference

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arXiv 2023年

作者： Gao, Yuan Liu, Weidong Wang, Hansheng Wang, Xiaozhou Yan, Yibo Zhang, Riquan School of Statistics Key Laboratory of Advanced Theory and Application in Statistics and Data Science - MOE East China Normal University Shanghai China School of Mathematical Sciences Key Lab of Artificial Intelligence - MOE Shanghai Jiao Tong University Shanghai China Guanghua School of Management Peking University Beijing China

The rapid emergence of massive datasets in various fields poses a serious challenge to traditional statistical methods. Meanwhile, it provides opportunities for researchers to develop novel algorithms. Inspired by the idea of divide-and-conquer, various distributed frameworks for statistical estimation and inference have been proposed. They were developed to deal with large-scale statistical optimization problems. This paper aims to provide a comprehensive review for related literature. It includes parametric models, nonparametric models, and other frequently used models. Their key ideas and theoretical properties are summarized. The trade-off between communication cost and estimate precision together with other concerns are discussed. Copyright © 2023, The Authors. All rights reserved.

关键词： Principal component analysis

Derivatives of local times for some Gaussian fields

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arXiv 2019年

作者： Hong, Minhao Xu, Fangjun School of Statistics East China Normal University Shanghai200262 China Key Laboratory of Advanced Theory and Application in Statistics and Data Science - MOE School of Statistics East China Normal University Shanghai200062 China NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai 3663 Zhongshan Road North Shanghai200062 China

In this article, we consider derivatives of local time for a (2, d)-Gaussian field Z = {Z(t, s) = XtH1 − XeH2 , s, t ≥ 0}, s where XH1 and XeH2 are two independent processes from a class of d-dimensional centered Gaussian processes satisfying certain local nondeterminism property. We first give a condition for existence of derivatives of the local time. Then, under this condition, we show that derivatives of the local time are Hölder continuous in both time and space variables. Moreover, under some additional assumptions, we show that this condition is also necessary for existence of derivatives of the local time at the origin. Copyright © 2019, The Authors. All rights reserved.

关键词： Gaussian distribution

Kernel entropy estimation for long memory linear processes with infinite variance

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arXiv 2022年

作者： Liu, Hui Xu, Fangjun School of Statistics East China Normal University Shanghai200262 China Key Laboratory of Advanced Theory and Application in Statistics and Data Science - MOE School of Statistics East China Normal University Shanghai200062 China NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai 3663 Zhongshan Road North Shanghai200062 China

Let X = {Xn : n ∈ N} be a long memory linear process with innovations in the domain of attraction of an α-stable law (0 RR f 2(x) dx by using the kernel estimator X 2 Tn(hn) = n(n − 1)hn 1≤jn K (Xih−nXj) . The simulation study for long memory linear processes with symmetric α-stable innovations is also given. © 2022, CC BY-NC-SA.

关键词： Probability density function

Derivatives of local times for some Gaussian fields II

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arXiv 2020年

Given a (2, d)-Gaussian field (formula presented), s where XH1 and XeH2 are independent d-dimensional centered Gaussian processes satisfying certain properties, we will give the necessary condition for existence of de... 详细信息

关键词： Gaussian distribution

A hybrid deep learning method for finite-horizon mean-field game problems

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arXiv 2023年

作者： Zhang, Yu Jin, Zhuo Wei, Jiaqin Yin, George Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE School of Statistics East China Normal University Shanghai200062 China Department of Actuarial Studies and Business Analytics Macquarie University NSW2109 Australia Department of Mathematics University of Connecticut Storrs CT06269-1009 United States

This paper develops a new deep learning algorithm to solve a class of finite-horizon mean-field games. The proposed hybrid algorithm uses Markov chain approximation method combined with a stochastic approximation-based iterative deep learning algorithm. Under the framework of finite-horizon mean-field games, the induced measure and Monte-Carlo algorithm are adopted to establish the iterative mean-field interaction in Markov chain approximation method and deep learning, respectively. The Markov chain approximation method plays a key role in constructing the iterative algorithm and estimating an initial value of a neural network, whereas stochastic approximation is used to find accurate parameters in a bounded region. The convergence of the hybrid algorithm is proved;two numerical examples are provided to illustrate the results. Copyright © 2023, The Authors. All rights reserved.

关键词： Markov chains

Mean-variance portfolio selection with dynamic attention behavior in a hidden Markov model

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arXiv 2022年

In this paper, we study closed-loop equilibrium strategies for mean-variance portfolio selection problem in a hidden Markov model with dynamic attention behavior. In addition to the investment strategy, the investor’s attention to news is introduced as a control of the accuracy of the news signal process. The objective is to find equilibrium strategies by numerically solving an extended HJB equation by using Markov chain approximation method. An iterative algorithm is constructed and its convergence is established. Numerical examples are also provided to illustrate the results. Copyright © 2022, The Authors. All rights reserved.

关键词： Hidden Markov models

HYPOTHESIS TEST ON A MIXTURE FORWARD-INCUBATION-TIME EPIDEMIC MODEL WITH application TO COVID-19 OUTBREAK

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arXiv 2022年

作者： Wang, Chunlin Li, Pengfei Liu, Yukun Zhou, Xiao-Hua Qin, Jing Department of Statistics and Data Science School of Economics Wang Yanan Institute for Studies in Economics MOE Key Lab of Econometrics Fujian Key Lab of Statistics Xiamen University Xiamen China Department of Statistics and Actuarial Sciences University of Waterloo Canada Key Laboratory of Advanced Theory and Application in Statistics and Data Science - MOE School of Statistics East China Normal University Shanghai China Department of Biostatistics School of Public Health Peking University Beijing China National Institute of Allergy and Infectious Diseases National Institutes of Health United States

The distribution of the incubation period of the novel coronavirus disease that emerged in 2019 (COVID-19) has crucial clinical implications for understanding this disease and devising effective disease-control measures. Qin et al. (2020) designed a cross-sectional and forward follow-up study to collect the duration times between a specific observation time and the onset of COVID-19 symptoms for a number of individuals. They further proposed a mixture forward-incubation-time epidemic model, which is a mixture of an incubation-period distribution and a forward time distribution, to model the collected duration times and to estimate the incubation-period distribution of COVID-19. In this paper, we provide sufficient conditions for the identifiability of the unknown parameters in the mixture forward-incubation-time epidemic model when the incubation period follows a two-parameter distribution. Under the same setup, we propose a likelihood ratio test (LRT) for testing the null hypothesis that the mixture forward-incubation-time epidemic model is a homogeneous exponential distribution. The testing problem is non-regular because a nuisance parameter is present only under the alternative. We establish the limiting distribution of the LRT and identify an explicit representation for it. The limiting distribution of the LRT under a sequence of local alternatives is also obtained. Our simulation results indicate that the LRT has desirable type I errors and powers, and we analyze a COVID-19 outbreak dataset from China to illustrate the usefulness of the LRT. Copyright © 2022, The Authors. All rights reserved.

关键词： COVID-19

Robust Online Detection in Serially Correlated Directed Network

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arXiv 2021年

作者： Yu, Miaomiao Zhou, Yuhao Tsung, Fugee Key Laboratory of Advanced Theory and Application in Statistics and Data Science MOE Academy of Statistics and Interdisciplinary Sciences East China Normal University Shanghai China Department of Statistics and Operations Research University of North Carolina at Chapel Hill Chapel HillNC27599 United States Department of Industrial Engineering and Decision Analytics Hong Kong University of Science and Technology Kowloon Hong Kong

As the complexity of production processes increases, the diversity of data types drives the development of network monitoring technology. This paper mainly focuses on an online algorithm to detect serially correlated directed networks robustly and sensitively. First, we consider a transition probability matrix to resolve the double correlation of primary data. Further, since the sum of each row of the transition probability matrix is one, it standardizes the data, facilitating subsequent modeling. Then we extend the spring length based method to the multivariate case and propose an adaptive cumulative sum (CUSUM) control chart on the strength of a weighted statistic to monitor directed networks. This novel approach assumes only that the process observation is associated with nearby points without any parametric time series model, which is in line with reality. Simulation results and a real example from metro transportation demonstrate the superiority of our design. Copyright © 2021, The Authors. All rights reserved.

关键词： Digital storage