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A study of orthogonal array-based designs under a broad class of space-filling criteria 广义空间填充准则下正交阵列设计的研究
The Annals of Statistics Pub Date : 2022-10-01 DOI: 10.1214/22-aos2215
Guanzhou Chen, Boxin Tang
{"title":"A study of orthogonal array-based designs under a broad class of space-filling criteria","authors":"Guanzhou Chen, Boxin Tang","doi":"10.1214/22-aos2215","DOIUrl":"https://doi.org/10.1214/22-aos2215","url":null,"abstract":"Space-filling designs based on orthogonal arrays are attractive for computer experiments for they can be easily generated with desirable low-dimensional stratification properties. Nonetheless, it is not very clear how they behave and how to construct good such designs under other space-filling criteria. In this paper, we justify orthogonal array-based designs under a broad class of space-filling criteria, which include commonly used distance-, orthogonality- and discrepancy-based measures. To identify designs with even better space-filling properties, we partition orthogonal array-based designs into classes by allowable level permutations and show that the average performance of each class of designs is determined by two types of stratifications, with one of them being achieved by strong orthogonal arrays of strength 2+. Based on these results, we investigate various new and exist-ing constructions of space-filling orthogonal array-based designs, including some strong orthogonal arrays of strength 2+ and mappable nearly orthogonal arrays.","PeriodicalId":22375,"journal":{"name":"The Annals of Statistics","volume":"339 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80741450","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}
引用次数: 1
Efficiency of estimators for locally asymptotically normal quantum statistical models 局部渐近正态量子统计模型估计量的效率
The Annals of Statistics Pub Date : 2022-09-02 DOI: 10.1214/23-aos2285
A. Fujiwara, Koichi Yamagata
{"title":"Efficiency of estimators for locally asymptotically normal quantum statistical models","authors":"A. Fujiwara, Koichi Yamagata","doi":"10.1214/23-aos2285","DOIUrl":"https://doi.org/10.1214/23-aos2285","url":null,"abstract":"We herein establish an asymptotic representation theorem for locally asymptotically normal quantum statistical models. This theorem enables us to study the asymptotic efficiency of quantum estimators such as quantum regular estimators and quantum minimax estimators, leading to a universal tight lower bound beyond the i.i.d. assumption. This formulation complements the theory of quantum contiguity developed in the previous paper [Fujiwara and Yamagata, Bernoulli 26 (2020) 2105-2141], providing a solid foundation of the theory of weak quantum local asymptotic normality.","PeriodicalId":22375,"journal":{"name":"The Annals of Statistics","volume":"51 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84640042","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}
引用次数: 1
On optimal block resampling for Gaussian-subordinated long-range dependent processes 高斯从属长程相关过程的最优块重采样
The Annals of Statistics Pub Date : 2022-08-02 DOI: 10.1214/22-aos2242
Qihao Zhang, S. Lahiri, D. Nordman
{"title":"On optimal block resampling for Gaussian-subordinated long-range dependent processes","authors":"Qihao Zhang, S. Lahiri, D. Nordman","doi":"10.1214/22-aos2242","DOIUrl":"https://doi.org/10.1214/22-aos2242","url":null,"abstract":"Block-based resampling estimators have been intensively investigated for weakly dependent time processes, which has helped to inform implementation (e.g., best block sizes). However, little is known about resampling performance and block sizes under strong or long-range dependence. To establish guideposts in block selection, we consider a broad class of strongly dependent time processes, formed by a transformation of a stationary long-memory Gaussian series, and examine block-based resampling estimators for the variance of the prototypical sample mean; extensions to general statistical functionals are also considered. Unlike weak dependence, the properties of resampling estimators under strong dependence are shown to depend intricately on the nature of non-linearity in the time series (beyond Hermite ranks) in addition the long-memory coefficient and block size. Additionally, the intuition has often been that optimal block sizes should be larger under strong dependence (say $O(n^{1/2})$ for a sample size $n$) than the optimal order $O(n^{1/3})$ known under weak dependence. This intuition turns out to be largely incorrect, though a block order $O(n^{1/2})$ may be reasonable (and even optimal) in many cases, owing to non-linearity in a long-memory time series. While optimal block sizes are more complex under long-range dependence compared to short-range, we provide a consistent data-driven rule for block selection, and numerical studies illustrate that the guides for block selection perform well in other block-based problems with long-memory time series, such as distribution estimation and strategies for testing Hermite rank.","PeriodicalId":22375,"journal":{"name":"The Annals of Statistics","volume":"117 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81076550","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}
引用次数: 2
Optimal signal detection in some spiked random matrix models: Likelihood ratio tests and linear spectral statistics 一些尖刺随机矩阵模型的最优信号检测:似然比检验和线性谱统计
The Annals of Statistics Pub Date : 2022-08-01 DOI: 10.1214/21-aos2150
Debapratim Banerjee, Zongming Ma
{"title":"Optimal signal detection in some spiked random matrix models: Likelihood ratio tests and linear spectral statistics","authors":"Debapratim Banerjee, Zongming Ma","doi":"10.1214/21-aos2150","DOIUrl":"https://doi.org/10.1214/21-aos2150","url":null,"abstract":"We study signal detection by likelihood ratio tests in a number of spiked random matrix models, including but not limited to Gaussian mixtures and spiked Wishart covariance matrices. We work directly with multi-spiked cases in these models and with flexible priors on signal components that allow dependence across spikes. We derive asymptotic normality for the log-likelihood ratios when the signal-tonoise ratios are below certain bounds. In addition, the log-likelihood ratios can be asymptotically decomposed as weighted sums of a collection of statistics which we call bipartite signed cycles. Based on this decomposition, we show that below the bounds we could always achieve the asymptotically optimal powers of likelihood ratio tests via tests based on linear spectral statistics which have polynomial time complexity.","PeriodicalId":22375,"journal":{"name":"The Annals of Statistics","volume":"52 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87239089","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}
引用次数: 1
Stochastic continuum-armed bandits with additive models: Minimax regrets and adaptive algorithm 具有加性模型的随机连续武装强盗:极小极大遗憾和自适应算法
The Annals of Statistics Pub Date : 2022-08-01 DOI: 10.1214/22-aos2182
T. Cai, Hongming Pu
{"title":"Stochastic continuum-armed bandits with additive models: Minimax regrets and adaptive algorithm","authors":"T. Cai, Hongming Pu","doi":"10.1214/22-aos2182","DOIUrl":"https://doi.org/10.1214/22-aos2182","url":null,"abstract":"We consider d -dimensional stochastic continuum-armed bandits with the expected reward function being additive β -H¨older with sparsity s for 0 < β < ∞ and 1 ≤ s ≤ d . The rate of convergence ˜ O ( s · T β +1 2 β +1 ) for the minimax regret is established where T is the number of rounds. In particular, the minimax regret does not depend on d and is linear in s . A novel algorithm is proposed and is shown to be rate-optimal, up to a logarithmic factor of T . The problem of adaptivity is also studied. A lower bound on the cost of adaptation to the smoothness is obtained and the result implies that adaptation for free is impossible in general without further structural assumptions. We then consider adaptive additive SCAB under an additional self-similarity assumption. An adaptive procedure is constructed and is shown to simultaneously achieve the minimax regret for a range of smoothness levels.","PeriodicalId":22375,"journal":{"name":"The Annals of Statistics","volume":"46 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84781752","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}
引用次数: 3
Limit theorems for distributions invariant under groups of transformations 变换群下分布不变的极限定理
The Annals of Statistics Pub Date : 2022-08-01 DOI: 10.1214/21-aos2165
Morgane Austern, Peter Orbanz
{"title":"Limit theorems for distributions invariant under groups of transformations","authors":"Morgane Austern, Peter Orbanz","doi":"10.1214/21-aos2165","DOIUrl":"https://doi.org/10.1214/21-aos2165","url":null,"abstract":"A distributional symmetry is invariance of a distribution under a group of transformations. Exchangeability and stationarity are examples. We explain that a result of ergodic theory provides a law of large numbers: If the group satisfies suitable conditions, expectations can be estimated by averaging over subsets of transformations, and these estimators are strongly consistent. We show that, if a mixing condition holds, the averages also satisfy a central limit theorem, a Berry-Esseen bound, and concentration. These are extended further to apply to triangular arrays, to randomly subsampled averages, and to a generalization of U-statistics. As applications, we obtain new results on exchangeability, random fields, network models, and a class of marked point processes. We also establish asymptotic normality of the empirical entropy for a large class of processes. Some known results are recovered as special cases, and can hence be interpreted as an outcome of symmetry. The proofs adapt Stein’s method.","PeriodicalId":22375,"journal":{"name":"The Annals of Statistics","volume":"238 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77012912","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}
引用次数: 6
Erratum: Asymptotic genealogies of interacting particle systems with an application to sequential Monte Carlo 勘误:相互作用粒子系统的渐近系谱及其在顺序蒙特卡罗中的应用
The Annals of Statistics Pub Date : 2022-08-01 DOI: 10.1214/21-aos2135
Jere Koskela, P. A. Jenkins, A. M. Johansen, Dario Spanò
{"title":"Erratum: Asymptotic genealogies of interacting particle systems with an application to sequential Monte Carlo","authors":"Jere Koskela, P. A. Jenkins, A. M. Johansen, Dario Spanò","doi":"10.1214/21-aos2135","DOIUrl":"https://doi.org/10.1214/21-aos2135","url":null,"abstract":"∗Supported by EPSRC grant EP/R044732/1. †Supported in part by funding from the Lloyd’s Register Foundation – Alan Turing Institute Programme on Data-Centric Engineering, and by EPSRC grants EP/R034710/1 and EP/T004134/1. ‡Also at the Department of Computer Science, University of Warwick. §Also at the Alan Turing Institute. MSC 2010 subject classifications: Primary 60E15; secondary 60G99, 62E20","PeriodicalId":22375,"journal":{"name":"The Annals of Statistics","volume":"280 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85222770","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}
引用次数: 1
Generalization error bounds of dynamic treatment regimes in penalized regression-based learning 基于惩罚回归学习的动态处理机制的泛化误差界限
The Annals of Statistics Pub Date : 2022-08-01 DOI: 10.1214/22-aos2171
E. J. Oh, Min Qian, Y. Cheung
{"title":"Generalization error bounds of dynamic treatment regimes in penalized regression-based learning","authors":"E. J. Oh, Min Qian, Y. Cheung","doi":"10.1214/22-aos2171","DOIUrl":"https://doi.org/10.1214/22-aos2171","url":null,"abstract":"","PeriodicalId":22375,"journal":{"name":"The Annals of Statistics","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84365667","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}
引用次数: 1
Distributed adaptive Gaussian mean estimation with unknown variance: Interactive protocol helps adaptation 具有未知方差的分布自适应高斯均值估计:交互式协议有助于自适应
The Annals of Statistics Pub Date : 2022-08-01 DOI: 10.1214/21-aos2167
T. Cai, Hongjie Wei
{"title":"Distributed adaptive Gaussian mean estimation with unknown variance: Interactive protocol helps adaptation","authors":"T. Cai, Hongjie Wei","doi":"10.1214/21-aos2167","DOIUrl":"https://doi.org/10.1214/21-aos2167","url":null,"abstract":"Distributed estimation of a Gaussian mean with unknown variance under communication constraints is studied. Necessary and sufficient communication costs under different types of distributed protocols are derived for any estimator that is adaptively rate-optimal over a range of possible values for the variance. Communication-efficient and statistically optimal procedures are developed. The analysis reveals an interesting and important distinction among different types of distributed protocols: compared to the independent protocols, interactive protocols such as the sequential and blackboard protocols require less communication costs for rate-optimal adaptive Gaussian mean estimation. The lower bound techniques developed in the present paper are novel and can be of independent interest. in this supplement the detailed proofs of Lemmas in the paper “Distributed Adaptive Gaussian Mean Estimation with Unknown Variance: Interactive Protocol Helps Adaptation”.","PeriodicalId":22375,"journal":{"name":"The Annals of Statistics","volume":"238 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79125682","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}
引用次数: 3
Optimal reach estimation and metric learning 最优到达估计和度量学习
The Annals of Statistics Pub Date : 2022-07-13 DOI: 10.1214/23-aos2281
Eddie Aamari, Cl'ement Berenfeld, Clément Levrard
{"title":"Optimal reach estimation and metric learning","authors":"Eddie Aamari, Cl'ement Berenfeld, Clément Levrard","doi":"10.1214/23-aos2281","DOIUrl":"https://doi.org/10.1214/23-aos2281","url":null,"abstract":"We study the estimation of the reach, an ubiquitous regularity parameter in manifold estimation and geometric data analysis. Given an i.i.d. sample over an unknown $d$-dimensional $mathcal{C}^k$-smooth submanifold of $mathbb{R}^D$, we provide optimal nonasymptotic bounds for the estimation of its reach. We build upon a formulation of the reach in terms of maximal curvature on one hand, and geodesic metric distortion on the other hand. The derived rates are adaptive, with rates depending on whether the reach of $M$ arises from curvature or from a bottleneck structure. In the process, we derive optimal geodesic metric estimation bounds.","PeriodicalId":22375,"journal":{"name":"The Annals of Statistics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88306929","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}
引用次数: 5
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