Annals of Statistics最新文献_第5页

Minimax estimation of smooth optimal transport maps 光滑最优运输图的极大极小估计

IF 4.5 1区数学

Annals of Statistics Pub Date : 2021-04-01 DOI: 10.1214/20-AOS1997

Jan-Christian Hütter, P. Rigollet

引用次数: 70

AVERAGE TREATMENT EFFECTS IN THE PRESENCE OF UNKNOWN INTERFERENCE. 在存在未知干扰的情况下的平均治疗效果。

IF 4.5 1区数学

Annals of Statistics Pub Date : 2021-04-01 Epub Date: 2021-04-02 DOI: 10.1214/20-aos1973

Fredrik Sävje, Peter Aronow, Michael Hudgens

引用次数: 0

Necessary and sufficient conditions for variable selection consistency of the LASSO in high dimensions 高维LASSO变量选择一致性的充分必要条件

IF 4.5 1区数学

Annals of Statistics Pub Date : 2021-04-01 DOI: 10.1214/20-AOS1979

S. Lahiri

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引用次数: 12

ASYMMETRY HELPS: EIGENVALUE AND EIGENVECTOR ANALYSES OF ASYMMETRICALLY PERTURBED LOW-RANK MATRICES. 不对称有助于：不对称扰动低阶矩阵的特征值和特征向量分析。

IF 4.5 1区数学

Annals of Statistics Pub Date : 2021-02-01 Epub Date: 2021-01-29 DOI: 10.1214/20-aos1963

Yuxin Chen, Chen Cheng, Jianqing Fan

{"title":"ASYMMETRY HELPS: EIGENVALUE AND EIGENVECTOR ANALYSES OF ASYMMETRICALLY PERTURBED LOW-RANK MATRICES.","authors":"Yuxin Chen, Chen Cheng, Jianqing Fan","doi":"10.1214/20-aos1963","DOIUrl":"10.1214/20-aos1963","url":null,"abstract":"This paper is concerned with the interplay between statistical asymmetry and spectral methods. Suppose we are interested in estimating a rank-1 and symmetric matrix <math> <mrow> <msup><mstyle><mi>M</mi></mstyle> <mo>⋆</mo></msup> <mo>∈</mo> <msup><mi>ℝ</mi> <mrow><mi>n</mi> <mo>×</mo> <mi>n</mi></mrow> </msup> </mrow> </math> , yet only a randomly perturbed version M is observed. The noise matrix M - M ⋆ is composed of independent (but not necessarily homoscedastic) entries and is, therefore, not symmetric in general. This might arise if, for example, we have two independent samples for each entry of M ⋆ and arrange them in an asymmetric fashion. The aim is to estimate the leading eigenvalue and the leading eigenvector of M ⋆. We demonstrate that the leading eigenvalue of the data matrix M can be <math><mrow><mi>O</mi> <mo>(</mo> <msqrt><mi>n</mi></msqrt> <mo>)</mo></mrow> </math> times more accurate (up to some log factor) than its (unadjusted) leading singular value of M in eigenvalue estimation. Moreover, the eigen-decomposition approach is fully adaptive to heteroscedasticity of noise, without the need of any prior knowledge about the noise distributions. In a nutshell, this curious phenomenon arises since the statistical asymmetry automatically mitigates the bias of the eigenvalue approach, thus eliminating the need of careful bias correction. Additionally, we develop appealing non-asymptotic eigenvector perturbation bounds; in particular, we are able to bound the perterbation of any linear function of the leading eigenvector of M (e.g. entrywise eigenvector perturbation). We also provide partial theory for the more general rank-r case. The takeaway message is this: arranging the data samples in an asymmetric manner and performing eigen-decomposition could sometimes be quite beneficial.","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":"49 1","pages":"435-458"},"PeriodicalIF":4.5,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8300484/pdf/nihms-1639565.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39218981","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A rule of thumb: Run lengths to false alarm of many types of control charts run in parallel on dependent streams are asymptotically independent 经验法则：在相关流上并行运行的许多类型的控制图的虚警运行长度是渐近独立的

IF 4.5 1区数学

Annals of Statistics Pub Date : 2021-02-01 DOI: 10.1214/20-AOS1968

M. Pollak

引用次数: 0

Wordlength enumerator for fractional factorial designs 分数阶乘设计的字长枚举器

IF 4.5 1区数学

Annals of Statistics Pub Date : 2021-02-01 DOI: 10.1214/20-AOS1955

Yu Tang, Hongquan Xu

引用次数: 4

Correction note: “Optimal two-stage procedures for estimating location and size of the maximum of a multivariate regression function” Ann. Statist. 40 (2012) 2850–2876 更正说明：“估计多元回归函数最大值的位置和大小的最佳两阶段程序”Ann.Statist。40（2012）2850–2876