Zhou Fan, Roy R. Lederman, Yi Sun, Tianhao Wang, Sheng Xu
{"title":"Maximum likelihood for high-noise group orbit estimation and single-particle cryo-EM","authors":"Zhou Fan, Roy R. Lederman, Yi Sun, Tianhao Wang, Sheng Xu","doi":"10.1214/23-aos2292","DOIUrl":"https://doi.org/10.1214/23-aos2292","url":null,"abstract":"","PeriodicalId":22375,"journal":{"name":"The Annals of Statistics","volume":"77 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140463015","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Changryong Baek, Marie-Christine Düker, V. Pipiras
{"title":"Local Whittle estimation of high-dimensional long-run variance and precision matrices","authors":"Changryong Baek, Marie-Christine Düker, V. Pipiras","doi":"10.1214/23-aos2330","DOIUrl":"https://doi.org/10.1214/23-aos2330","url":null,"abstract":"","PeriodicalId":22375,"journal":{"name":"The Annals of Statistics","volume":"158 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138987119","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We propose a concept of quantiles for probability measures on the unit hypersphere S d − 1 of R d . The innermost quantile is the Fréchet median, that is, the L 1 -analog of the Fréchet mean. The proposed quantiles μ mα,u are directional in nature: they are indexed by a scalar order α ∈ [ 0 , 1 ] and a unit vector u in the tangent space T m S d − 1 to S d − 1 at m . To ensure computability in any dimension d , our quantiles are essentially obtained by considering the Euclidean (Chaudhuri ( J. Amer. Statist. Assoc. 91 (1996) 862–872)) spatial quantiles in a suitable stereographic projection of S d − 1 onto T m S d − 1 . Despite this link with Euclidean spatial quantiles, studying the proposed spherical quantiles requires understanding the nature of the (Chaudhuri (1996)) quantiles in a version of the projective space where all points at infinity are identified. We thoroughly investigate the structural properties of our quan-tiles and we further study the asymptotic behavior of their sample versions, which requires controlling the impact of estimating m . Our spherical quantile concept also allows for companion concepts of ranks and depth on the hy-persphere. We illustrate the relevance of our construction by considering two inferential applications, related to supervised classification and to testing for rotational symmetry.
我们为 R d 的单位超球 S d - 1 上的概率度量提出了量值的概念。最内层的量值是弗雷谢特中值，即弗雷谢特均值的 L 1 类似值。建议的量化值 μ mα,u 具有方向性：它们由标量阶 α∈ [ 0 , 1 ] 和切线空间 T m S d - 1 中的单位向量 u 在 m 处与 S d - 1 进行索引。为了确保在任何维度 d 中的可计算性，我们的量纲基本上是通过考虑欧几里得（Chaudhuri ( J. Amer. Statist.Statist.Assoc. 91 (1996) 862-872)）的空间定量在 S d - 1 到 T m S d - 1 的合适立体投影中得到。尽管与欧几里得空间定量有这种联系，但要研究所提出的球面定量，就必须了解（乔杜里（1996））定量在投影空间版本中的性质，在这个版本中，所有的同位点都是确定的。我们深入研究了我们的量化模型的结构特性，并进一步研究了其样本版本的渐近行为，这需要控制估计 m 的影响。我们的球面量化概念还允许在 hy 球面上使用等级和深度的辅助概念。我们通过考虑与监督分类和旋转对称性测试相关的两个推理应用来说明我们的构造的相关性。
{"title":"Spatial quantiles on the hypersphere","authors":"Dimitri Konen, D. Paindaveine","doi":"10.1214/23-aos2332","DOIUrl":"https://doi.org/10.1214/23-aos2332","url":null,"abstract":"We propose a concept of quantiles for probability measures on the unit hypersphere S d − 1 of R d . The innermost quantile is the Fréchet median, that is, the L 1 -analog of the Fréchet mean. The proposed quantiles μ mα,u are directional in nature: they are indexed by a scalar order α ∈ [ 0 , 1 ] and a unit vector u in the tangent space T m S d − 1 to S d − 1 at m . To ensure computability in any dimension d , our quantiles are essentially obtained by considering the Euclidean (Chaudhuri ( J. Amer. Statist. Assoc. 91 (1996) 862–872)) spatial quantiles in a suitable stereographic projection of S d − 1 onto T m S d − 1 . Despite this link with Euclidean spatial quantiles, studying the proposed spherical quantiles requires understanding the nature of the (Chaudhuri (1996)) quantiles in a version of the projective space where all points at infinity are identified. We thoroughly investigate the structural properties of our quan-tiles and we further study the asymptotic behavior of their sample versions, which requires controlling the impact of estimating m . Our spherical quantile concept also allows for companion concepts of ranks and depth on the hy-persphere. We illustrate the relevance of our construction by considering two inferential applications, related to supervised classification and to testing for rotational symmetry.","PeriodicalId":22375,"journal":{"name":"The Annals of Statistics","volume":"52 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139331092","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Efficient estimation of the maximal association between multiple predictors and a survival outcome","authors":"T. Huang, Alex Luedtke, I. McKeague","doi":"10.1214/23-aos2313","DOIUrl":"https://doi.org/10.1214/23-aos2313","url":null,"abstract":"","PeriodicalId":22375,"journal":{"name":"The Annals of Statistics","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139326412","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper considers one-sample testing of a high-dimensional covariance matrix by deriving the detection boundary as a function of the signal sparsity and signal strength under the sparse alternative hypotheses. It first shows that the optimal detection boundary for testing sparse means is the minimax detection lower boundary for testing the covariance matrix. A multilevel thresholding test is proposed and is shown to be able to attain the detection lower boundary over a substantial range of the sparsity parameter, implying that the multilevel thresholding test is sharp optimal in the minimax sense over the range. The asymptotic distribution of the multilevel thresh-olding statistic for covariance matrices is derived under both Gaussian and non-Gaussian distributions by developing a novel U -statistic decomposition in conjunction with the matrix blocking and the coupling techniques to handle the complex dependence among the elements of the sample covariance matrix. The superiority in the detection boundary of the multilevel thresholding test over the existing tests is also demonstrated.
本文考虑了高维协方差矩阵的单样本测试，推导出了作为稀疏替代假设下信号稀疏度和信号强度函数的检测边界。它首先表明，检测稀疏均值的最佳检测边界是检测协方差矩阵的最小检测下边界。研究提出了一种多层次阈值检验，并证明它能在稀疏参数的很大范围内达到检测下限，这意味着多层次阈值检验在这个范围内是最小最优的。为了处理样本协方差矩阵元素之间的复杂依赖关系，结合矩阵阻塞和耦合技术，通过开发一种新颖的 U 统计分解，得出了协方差矩阵的多级阈值老化统计量在高斯和非高斯分布下的渐近分布。此外，还证明了多级阈值检验的检测边界优于现有检验。
{"title":"Sharp optimality for high-dimensional covariance testing under sparse signals","authors":"S. Chen, Yumou Qiu, Shuyi Zhang","doi":"10.1214/23-aos2310","DOIUrl":"https://doi.org/10.1214/23-aos2310","url":null,"abstract":"This paper considers one-sample testing of a high-dimensional covariance matrix by deriving the detection boundary as a function of the signal sparsity and signal strength under the sparse alternative hypotheses. It first shows that the optimal detection boundary for testing sparse means is the minimax detection lower boundary for testing the covariance matrix. A multilevel thresholding test is proposed and is shown to be able to attain the detection lower boundary over a substantial range of the sparsity parameter, implying that the multilevel thresholding test is sharp optimal in the minimax sense over the range. The asymptotic distribution of the multilevel thresh-olding statistic for covariance matrices is derived under both Gaussian and non-Gaussian distributions by developing a novel U -statistic decomposition in conjunction with the matrix blocking and the coupling techniques to handle the complex dependence among the elements of the sample covariance matrix. The superiority in the detection boundary of the multilevel thresholding test over the existing tests is also demonstrated.","PeriodicalId":22375,"journal":{"name":"The Annals of Statistics","volume":"62 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139328977","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Nonparametric inference on tail conditional quantiles and their least squares analogs, expectiles, remains limited to i.i.d. data. We develop a fully operational inferential theory for extreme conditional quantiles and expec-tiles in the challenging framework of α − mixing, conditional heavy-tailed data whose tail index may vary with covariate values. This requires a dedicated treatment to deal with data sparsity in the far tail of the response, in addition to handling difficulties inherent to mixing, smoothing, and sparsity associated to covariate localization. We prove the pointwise asymptotic normality of our estimators and obtain optimal rates of convergence reminiscent of those found in the i.i.d. regression setting, but which had not been established in the conditional extreme value literature. Our assumptions hold in a wide range of models. We propose full bias and variance reduction procedures, and simple but effective data-based rules for selecting tuning hyperpa-rameters. Our inference strategy is shown to perform well in finite samples and is showcased in applications to stock returns and tornado loss data.
{"title":"Inference for extremal regression with dependent heavy-tailed data","authors":"A. Daouia, Gilles Stupfler, A. Usseglio‐Carleve","doi":"10.1214/23-aos2320","DOIUrl":"https://doi.org/10.1214/23-aos2320","url":null,"abstract":"Nonparametric inference on tail conditional quantiles and their least squares analogs, expectiles, remains limited to i.i.d. data. We develop a fully operational inferential theory for extreme conditional quantiles and expec-tiles in the challenging framework of α − mixing, conditional heavy-tailed data whose tail index may vary with covariate values. This requires a dedicated treatment to deal with data sparsity in the far tail of the response, in addition to handling difficulties inherent to mixing, smoothing, and sparsity associated to covariate localization. We prove the pointwise asymptotic normality of our estimators and obtain optimal rates of convergence reminiscent of those found in the i.i.d. regression setting, but which had not been established in the conditional extreme value literature. Our assumptions hold in a wide range of models. We propose full bias and variance reduction procedures, and simple but effective data-based rules for selecting tuning hyperpa-rameters. Our inference strategy is shown to perform well in finite samples and is showcased in applications to stock returns and tornado loss data.","PeriodicalId":22375,"journal":{"name":"The Annals of Statistics","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139330311","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
F. Telschow, Dan Cheng, Pratyush Pranav, Armin Schwartzman
{"title":"Estimation of expected Euler characteristic curves of nonstationary smooth random fields","authors":"F. Telschow, Dan Cheng, Pratyush Pranav, Armin Schwartzman","doi":"10.1214/23-aos2337","DOIUrl":"https://doi.org/10.1214/23-aos2337","url":null,"abstract":"","PeriodicalId":22375,"journal":{"name":"The Annals of Statistics","volume":"61 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139328491","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Finite-sample complexity of sequential Monte Carlo estimators","authors":"J. Marion, Joseph Mathews, S. Schmidler","doi":"10.1214/23-aos2295","DOIUrl":"https://doi.org/10.1214/23-aos2295","url":null,"abstract":"","PeriodicalId":22375,"journal":{"name":"The Annals of Statistics","volume":"80 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74408258","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A. Weinstein, Weijie J. Su, M. Bogdan, Rina Foygel Barber, E. Candès
{"title":"A power analysis for model-X knockoffs with ℓp-regularized statistics","authors":"A. Weinstein, Weijie J. Su, M. Bogdan, Rina Foygel Barber, E. Candès","doi":"10.1214/23-aos2274","DOIUrl":"https://doi.org/10.1214/23-aos2274","url":null,"abstract":"","PeriodicalId":22375,"journal":{"name":"The Annals of Statistics","volume":"45 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77963464","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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