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Statistics & Probability
Runze Li, Kai Xu, Yeqing Zhou, Liping Zhu
Summary: In this article, we propose a novel test based on an aggregation of the marginal cumulative covariances to accommodate heteroscedasticity and high dimensionality in high-dimensional data. Our proposed test statistic is scale-invariance, tuning-free, and easy to implement, with established asymptotic normality under the null hypothesis. We find that our proposed test is much more powerful than existing competitors for covariates with heterogeneous variances, even under high-dimensional linear models, while maintaining high efficiency for homoscedastic covariates.
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
(2023)
Article
Statistics & Probability
Zhendong Wang, Xingzhong Xu
Summary: With the emergence of the big data era, testing high dimensional covariance matrices has become a prominent area in contemporary statistical inference. A novel test based on posterior Bayes factor is proposed in this paper for the identification and sphericity testing. The research shows that the new test outperforms some well-known tests in terms of Type I error rate and empirical power under general alternatives.
JOURNAL OF MULTIVARIATE ANALYSIS
(2021)
Article
Statistics & Probability
Hao Chen, Yin Xia
Summary: This article introduces a statistical method for high-dimensional data that uses nearest neighbor information for nonparametric testing. The method effectively controls Type I error and exhibits good performance as the dimension increases with sample size.
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
(2023)
Article
Economics
Xinxin Yang, Xinghua Zheng, Jiaqi Chen
Summary: Tests for high-dimensional covariance matrices based on a generalized elliptical model are developed, without assuming specific parametric distributions or involving data kurtosis. These tests can be used to test uncorrelatedness among idiosyncratic returns, demonstrating their flexibility and applicability.
JOURNAL OF ECONOMETRICS
(2021)
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Mathematics, Applied
Guili Liao, Liang Peng, Rongmao Zhang
Summary: The paper proposes a new method for testing the equality of covariance matrices, which is not affected by dimension divergence and shows stable performance and higher power in simulation studies. The method is further illustrated using a breast cancer dataset.
SCIENCE CHINA-MATHEMATICS
(2021)
Article
Biology
Long Yu, Jiahui Xie, Wang Zhou
Summary: In this paper, we propose test statistics for the Kronecker product covariance matrix based on linear spectral statistics of renormalized sample covariance matrices. A central limit theorem is proved for the linear spectral statistics, with explicit formulas for the mean and covariance functions, thereby filling a gap in the literature. We then show theoretically that the proposed test statistics have well-controlled size and high power. We further propose a bootstrap resampling algorithm to approximate the limiting distributions of the associated linear spectral statistics. Consistency of the bootstrap procedure is guaranteed under mild conditions. The proposed test procedure is also applicable to the Kronecker product covariance model with additional random noise. In our simulations, the empirical sizes of the proposed test procedure and its bootstrapped version are close to the corresponding theoretical values, while the power converges to 1 quickly as the dimension and sample size increase.
Article
Statistics & Probability
Tingyu Lai, Zhongzhan Zhang, Yafei Wang, Linglong Kong
Summary: A new nonparametric independence test for two functional random variables is proposed, utilizing the angle covariance metric. The test shows desirable properties and can be applied to functional data without finite moment conditions. Simulation results demonstrate that the test outperforms other competing tests for functional data.
JOURNAL OF MULTIVARIATE ANALYSIS
(2021)
Article
Biology
Maomao Ding, Ruosha Li, Jin Qin, Jing Ning
Summary: This paper proposes a double-robust test to evaluate the dependence of gene expression levels in a gene coexpression network on clinical information, and it demonstrates computational efficiency and robustness with respect to model assumptions.
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Automation & Control Systems
Hanjia Gao, Xiaofeng Shao
Summary: This paper investigates the behavior of sample MMD in a high-dimensional environment and proposes a new studentized test statistic. Central limit theorems and convergence rates are derived for studentized sample MMD, suggesting that the accuracy of normal approximation improves with dimensionality. The paper also provides a general theory on power analysis and shows the effectiveness of the proposed test in moderately high dimensional regime.
JOURNAL OF MACHINE LEARNING RESEARCH
(2023)
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Computer Science, Artificial Intelligence
Necla Kochan, G. Yazgi Tutuncu, Goknur Giner
Summary: This study introduces a new approach based on local dependence function to estimate covariance matrix in order to improve the classification performance of RNA-Seq data sets. This new method assumes that dependencies between genes are locally defined rather than completely dependent.
EXPERT SYSTEMS WITH APPLICATIONS
(2021)
Article
Biochemical Research Methods
Omid Abbaszadeh, Ali Azarpeyvand, Alireza Khanteymoori, Abbas Bahari
Summary: This paper proposes two new algorithms for reconstructing a gene network from expression profiles with and without prior knowledge in small sample and high-dimensional settings. Experimental results show that the proposed algorithms achieve better results in terms of both PR and ROC curves compared to state-of-the-art methods.
IEEE-ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS
(2022)
Article
Computer Science, Information Systems
Salem Said, Simon Heuveline, Cyrus Mostajeran
Summary: This paper establishes an unexpected connection between Riemannian Gaussian distributions and random matrix theory, proving the equivalence of these distributions to certain matrix ensembles. It provides a highly efficient approximation for computing the normalizing factors of Riemannian Gaussian distributions on high-dimensional covariance matrices. Numerical experiments demonstrate the usefulness of this approximation for real-world datasets.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2023)
Article
Economics
Long Yu, Yong He, Xinbing Kong, Xinsheng Zhang
Summary: This study introduces a projection estimation method for large-dimensional matrix factor models, showing faster convergence rates and asymptotic distributions compared to existing estimators. By linearly filtering idiosyncratic error components, the method simplifies factor analysis and increases the signal-to-noise ratio.
JOURNAL OF ECONOMETRICS
(2022)
Article
Multidisciplinary Sciences
Jose Jairo Santana-e-Silva, Francisco Cribari-Neto, Klaus L. P. Vasconcellos
Summary: The beta distribution is commonly used to model variables in (0, 1). This paper examines its adequacy and tests the hypothesis using information matrix equality. The results show that the beta distribution performs well in representing Covid-19 death rates, especially when considering the impact of vaccination.
Article
Mathematical & Computational Biology
Nan Sun, Cheng Yong Tang
Summary: This study proposes a method to address the challenging task of testing the equality between two high-dimensional covariance matrices. It involves randomly projecting the original data to a lower-dimensional space and applying corrected likelihood ratio tests based on random matrix theory. Through evaluating the power function, the study shows that this method is more powerful in detecting unequal covariance matrices with small component-wise discrepancy.
STATISTICS AND ITS INTERFACE
(2022)
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Statistics & Probability
Damien Passemier, Zhaoyuan Li, Jianfeng Yao
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
(2017)
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Statistics & Probability
Weiming Li, Jianfeng Yao
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
(2018)
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Engineering, Industrial
Jiaqi Chen, Hualong Yang, Jianfeng Yao
QUALITY TECHNOLOGY AND QUANTITATIVE MANAGEMENT
(2018)
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Computer Science, Interdisciplinary Applications
Keren Shen, Jianfeng Yao, Wai Keung Li
COMPUTATIONAL STATISTICS & DATA ANALYSIS
(2019)
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Business, Finance
Keren Shen, Jianfeng Yao, Wai Keung Li
QUANTITATIVE FINANCE
(2020)
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Statistics & Probability
Weiming Li, Zeng Li, Jianfeng Yao
SCANDINAVIAN JOURNAL OF STATISTICS
(2018)
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Mathematical & Computational Biology
Keren Shen, Jianfeng Yao, Wai Keung Li
STATISTICS AND ITS INTERFACE
(2018)
Book Review
Mathematics, Interdisciplinary Applications
Jianfeng Yao
JOURNAL OF TIME SERIES ANALYSIS
(2019)
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Statistics & Probability
Zeng Li, Clifford Lam, Jianfeng Yao, Qiwei Yao
ANNALS OF STATISTICS
(2019)
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Mathematics, Applied
Yuyang Xu, Jianfeng Yao
LINEAR ALGEBRA AND ITS APPLICATIONS
(2020)
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Statistics & Probability
Jian Song, Jianfeng Yao, Wangjun Yuan
ANNALS OF APPLIED PROBABILITY
(2020)
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Statistics & Probability
Zeng Li, Fang Han, Jianfeng Yao
ANNALS OF STATISTICS
(2020)
Article
Statistics & Probability
Jian Song, Jianfeng Yao, Wangjun Yuan
Summary: This survey reviews a selection of results on the eigenvalues of stochastic processes from the literature of the past three decades, and discusses the eigenvalues of recent variations of such processes.
JOURNAL OF MULTIVARIATE ANALYSIS
(2022)
Article
Economics
Zhaoyuan Li, Jianfeng Yao
ECONOMETRICS AND STATISTICS
(2019)
Article
Statistics & Probability
Jiaqi Chen, Hualong Yang, Jianfeng Yao
COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION
(2018)