Annals of Statistics最新文献

ON BLOCKWISE AND REFERENCE PANEL-BASED ESTIMATORS FOR GENETIC DATA PREDICTION IN HIGH DIMENSIONS. 高维度遗传数据预测的基于 blockwise 和参考面板的估计器。

IF 3.2 1区数学

Annals of Statistics Pub Date : 2024-06-01 Epub Date: 2024-08-11 DOI: 10.1214/24-aos2378

Bingxin Zhao, Shurong Zheng, Hongtu Zhu

{"title":"ON BLOCKWISE AND REFERENCE PANEL-BASED ESTIMATORS FOR GENETIC DATA PREDICTION IN HIGH DIMENSIONS.","authors":"Bingxin Zhao, Shurong Zheng, Hongtu Zhu","doi":"10.1214/24-aos2378","DOIUrl":"10.1214/24-aos2378","url":null,"abstract":"Genetic prediction holds immense promise for translating genetic discoveries into medical advances. As the high-dimensional covariance matrix (or the linkage disequilibrium (LD) pattern) of genetic variants often presents a block-diagonal structure, numerous methods account for the dependence among variants in predetermined local LD blocks. Moreover, due to privacy considerations and data protection concerns, genetic variant dependence in each LD block is typically estimated from external reference panels rather than the original training data set. This paper presents a unified analysis of blockwise and reference panel-based estimators in a high-dimensional prediction framework without sparsity restrictions. We find that, surprisingly, even when the covariance matrix has a block-diagonal structure with well-defined boundaries, blockwise estimation methods adjusting for local dependence can be substantially less accurate than methods controlling for the whole covariance matrix. Further, estimation methods built on the original training data set and external reference panels are likely to have varying performance in high dimensions, which may reflect the cost of having only access to summary level data from the training data set. This analysis is based on novel results in random matrix theory for block-diagonal covariance matrix. We numerically evaluate our results using extensive simulations and real data analysis in the UK Biobank.","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":null,"pages":null},"PeriodicalIF":3.2,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11391480/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142279682","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

RANK-BASED INDICES FOR TESTING INDEPENDENCE BETWEEN TWO HIGH-DIMENSIONAL VECTORS. 基于秩的指数，用于测试两个高维向量之间的独立性。

IF 4.5 1区数学

Annals of Statistics Pub Date : 2024-02-01 Epub Date: 2024-03-07 DOI: 10.1214/23-aos2339

Yeqing Zhou, Kai Xu, Liping Zhu, Runze Li

{"title":"RANK-BASED INDICES FOR TESTING INDEPENDENCE BETWEEN TWO HIGH-DIMENSIONAL VECTORS.","authors":"Yeqing Zhou, Kai Xu, Liping Zhu, Runze Li","doi":"10.1214/23-aos2339","DOIUrl":"10.1214/23-aos2339","url":null,"abstract":"To test independence between two high-dimensional random vectors, we propose three tests based on the rank-based indices derived from Hoeffding's <math><mi>D</mi></math>, Blum-Kiefer-Rosenblatt's <math><mi>R</mi></math> and Bergsma-Dassios-Yanagimoto's <math><msup><mrow><mi>τ</mi></mrow><mrow><mo>*</mo></mrow></msup></math>. Under the null hypothesis of independence, we show that the distributions of the proposed test statistics converge to normal ones if the dimensions diverge arbitrarily with the sample size. We further derive an explicit rate of convergence. Thanks to the monotone transformation-invariant property, these distribution-free tests can be readily used to generally distributed random vectors including heavily tailed ones. We further study the local power of the proposed tests and compare their relative efficiencies with two classic distance covariance/correlation based tests in high dimensional settings. We establish explicit relationships between <math><mi>D</mi><mo>,</mo><mi>R</mi><mo>,</mo><msup><mrow><mi>τ</mi></mrow><mrow><mo>*</mo></mrow></msup></math> and Pearson's correlation for bivariate normal random variables. The relationships serve as a basis for power comparison. Our theoretical results show that under a Gaussian equicorrelation alternative, (i) the proposed tests are superior to the two classic distance covariance/correlation based tests if the components of random vectors have very different scales; (ii) the asymptotic efficiency of the proposed tests based on <math><mi>D</mi><mo>,</mo><msup><mrow><mi>τ</mi></mrow><mrow><mo>*</mo></mrow></msup></math> and <math><mi>R</mi></math> are sorted in a descending order.","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":null,"pages":null},"PeriodicalIF":4.5,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11064990/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140849012","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

Order-of-addition orthogonal arrays to study the effect of treatment ordering 研究正交加法排序对处理排序的影响

1区数学

Annals of Statistics Pub Date : 2023-08-01 DOI: 10.1214/23-aos2317

Eric D. Schoen, Robert W. Mee

引用次数: 0

Matching recovery threshold for correlated random graphs 相关随机图的匹配恢复阈值

1区数学

Annals of Statistics Pub Date : 2023-08-01 DOI: 10.1214/23-aos2305

Jian Ding, Hang Du

引用次数: 13

Post-selection inference via algorithmic stability 通过算法稳定性进行后选择推理

1区数学

Annals of Statistics Pub Date : 2023-08-01 DOI: 10.1214/23-aos2303

Tijana Zrnic, Michael I. Jordan

引用次数: 2

Statistical inference on a changing extreme value dependence structure 变化极值依赖结构的统计推断

1区数学

Annals of Statistics Pub Date : 2023-08-01 DOI: 10.1214/23-aos2314

Holger Drees

引用次数: 2

Bridging factor and sparse models 桥接因子与稀疏模型

1区数学

Annals of Statistics Pub Date : 2023-08-01 DOI: 10.1214/23-aos2304

Jianqing Fan, Ricardo Masini, Marcelo C. Medeiros

引用次数: 0

Projected state-action balancing weights for offline reinforcement learning 用于离线强化学习的预估状态-行为平衡权值

1区数学

Annals of Statistics Pub Date : 2023-08-01 DOI: 10.1214/23-aos2302

Jiayi Wang, Zhengling Qi, Raymond K. W. Wong

{"title":"Projected state-action balancing weights for offline reinforcement learning","authors":"Jiayi Wang, Zhengling Qi, Raymond K. W. Wong","doi":"10.1214/23-aos2302","DOIUrl":"https://doi.org/10.1214/23-aos2302","url":null,"abstract":"Off-policy evaluation is considered a fundamental and challenging problem in reinforcement learning (RL). This paper focuses on value estimation of a target policy based on pre-collected data generated from a possibly different policy, under the framework of infinite-horizon Markov decision processes. Motivated by the recently developed marginal importance sampling method in RL and the covariate balancing idea in causal inference, we propose a novel estimator with approximately projected state-action balancing weights for the policy value estimation. We obtain the convergence rate of these weights, and show that the proposed value estimator is asymptotically normal under technical conditions. In terms of asymptotics, our results scale with both the number of trajectories and the number of decision points at each trajectory. As such, consistency can still be achieved with a limited number of subjects when the number of decision points diverges. In addition, we develop a necessary and sufficient condition for establishing the well-posedness of the operator that relates to the nonparametric Q-function estimation in the off-policy setting, which characterizes the difficulty of Q-function estimation and may be of independent interest. Numerical experiments demonstrate the promising performance of our proposed estimator.","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135055878","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 6

A cross-validation framework for signal denoising with applications to trend filtering, dyadic CART and beyond 一个用于信号去噪的交叉验证框架，应用于趋势滤波，二元CART等

1区数学

Annals of Statistics Pub Date : 2023-08-01 DOI: 10.1214/23-aos2283

Anamitra Chaudhuri, Sabyasachi Chatterjee

引用次数: 0

Relaxing the i.i.d. assumption: Adaptively minimax optimal regret via root-entropic regularization 放宽i.i.d假设:基于根熵正则化的自适应最小最大最优后悔

1区数学

Annals of Statistics Pub Date : 2023-08-01 DOI: 10.1214/23-aos2315

Blair Bilodeau, Jeffrey Negrea, Daniel M. Roy

{"title":"Relaxing the i.i.d. assumption: Adaptively minimax optimal regret via root-entropic regularization","authors":"Blair Bilodeau, Jeffrey Negrea, Daniel M. Roy","doi":"10.1214/23-aos2315","DOIUrl":"https://doi.org/10.1214/23-aos2315","url":null,"abstract":"We consider prediction with expert advice when data are generated from distributions varying arbitrarily within an unknown constraint set. This semi-adversarial setting includes (at the extremes) the classical i.i.d. setting, when the unknown constraint set is restricted to be a singleton, and the unconstrained adversarial setting, when the constraint set is the set of all distributions. The Hedge algorithm—long known to be minimax (rate) optimal in the adversarial regime—was recently shown to be simultaneously minimax optimal for i.i.d. data. In this work, we propose to relax the i.i.d. assumption by seeking adaptivity at all levels of a natural ordering on constraint sets. We provide matching upper and lower bounds on the minimax regret at all levels, show that Hedge with deterministic learning rates is suboptimal outside of the extremes and prove that one can adaptively obtain minimax regret at all levels. We achieve this optimal adaptivity using the follow-the-regularized-leader (FTRL) framework, with a novel adaptive regularization scheme that implicitly scales as the square root of the entropy of the current predictive distribution, rather than the entropy of the initial predictive distribution. Finally, we provide novel technical tools to study the statistical performance of FTRL along the semi-adversarial spectrum.","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135165186","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 7