Annals of Statistics最新文献_第3页

Inference on the maximal rank of time-varying covariance matrices using high-frequency data 基于高频数据的时变协方差矩阵最大秩的推断

1区数学

Annals of Statistics Pub Date : 2023-04-01 DOI: 10.1214/23-aos2273

Markus Reiss, Lars Winkelmann

引用次数: 0

Optimally tackling covariate shift in RKHS-based nonparametric regression 基于rkhs的非参数回归中协变量移位的优化处理

1区数学

Annals of Statistics Pub Date : 2023-04-01 DOI: 10.1214/23-aos2268

Cong Ma, Reese Pathak, Martin J. Wainwright

{"title":"Optimally tackling covariate shift in RKHS-based nonparametric regression","authors":"Cong Ma, Reese Pathak, Martin J. Wainwright","doi":"10.1214/23-aos2268","DOIUrl":"https://doi.org/10.1214/23-aos2268","url":null,"abstract":"We study the covariate shift problem in the context of nonparametric regression over a reproducing kernel Hilbert space (RKHS). We focus on two natural families of covariate shift problems defined using the likelihood ratios between the source and target distributions. When the likelihood ratios are uniformly bounded, we prove that the kernel ridge regression (KRR) estimator with a carefully chosen regularization parameter is minimax rate-optimal (up to a log factor) for a large family of RKHSs with regular kernel eigenvalues. Interestingly, KRR does not require full knowledge of the likelihood ratio apart from an upper bound on it. In striking contrast to the standard statistical setting without covariate shift, we also demonstrate that a naïve estimator, which minimizes the empirical risk over the function class, is strictly suboptimal under covariate shift as compared to KRR. We then address the larger class of covariate shift problems where likelihood ratio is possibly unbounded yet has a finite second moment. Here, we propose a reweighted KRR estimator that weights samples based on a careful truncation of the likelihood ratios. Again, we are able to show that this estimator is minimax optimal, up to logarithmic factors.","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135673416","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: 0

On high-dimensional Poisson models with measurement error: Hypothesis testing for nonlinear nonconvex optimization. 具有测量误差的高维泊松模型:非线性非凸优化的假设检验。

IF 4.5 1区数学

Annals of Statistics Pub Date : 2023-02-01 DOI: 10.1214/22-aos2248

Fei Jiang, Yeqing Zhou, Jianxuan Liu, Yanyuan Ma

{"title":"On high-dimensional Poisson models with measurement error: Hypothesis testing for nonlinear nonconvex optimization.","authors":"Fei Jiang, Yeqing Zhou, Jianxuan Liu, Yanyuan Ma","doi":"10.1214/22-aos2248","DOIUrl":"https://doi.org/10.1214/22-aos2248","url":null,"abstract":"We study estimation and testing in the Poisson regression model with noisy high dimensional covariates, which has wide applications in analyzing noisy big data. Correcting for the estimation bias due to the covariate noise leads to a non-convex target function to minimize. Treating the high dimensional issue further leads us to augment an amenable penalty term to the target function. We propose to estimate the regression parameter through minimizing the penalized target function. We derive the L1 and L2 convergence rates of the estimator and prove the variable selection consistency. We further establish the asymptotic normality of any subset of the parameters, where the subset can have infinitely many components as long as its cardinality grows sufficiently slow. We develop Wald and score tests based on the asymptotic normality of the estimator, which permits testing of linear functions of the members if the subset. We examine the finite sample performance of the proposed tests by extensive simulation. Finally, the proposed method is successfully applied to the Alzheimer's Disease Neuroimaging Initiative study, which motivated this work initially.","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":null,"pages":null},"PeriodicalIF":4.5,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10438917/pdf/nihms-1868138.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10054730","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

On High dimensional Poisson models with measurement error: hypothesis testing for nonlinear nonconvex optimization 具有测量误差的高维泊松模型:非线性非凸优化的假设检验

IF 4.5 1区数学

Annals of Statistics Pub Date : 2022-12-31 DOI: 10.48550/arXiv.2301.00139

Fei Jiang, Yeqing Zhou, Jianxuan Liu, Yanyuan Ma

{"title":"On High dimensional Poisson models with measurement error: hypothesis testing for nonlinear nonconvex optimization","authors":"Fei Jiang, Yeqing Zhou, Jianxuan Liu, Yanyuan Ma","doi":"10.48550/arXiv.2301.00139","DOIUrl":"https://doi.org/10.48550/arXiv.2301.00139","url":null,"abstract":"We study estimation and testing in the Poisson regression model with noisy high dimensional covariates, which has wide applications in analyzing noisy big data. Correcting for the estimation bias due to the covariate noise leads to a non-convex target function to minimize. Treating the high dimensional issue further leads us to augment an amenable penalty term to the target function. We propose to estimate the regression parameter through minimizing the penalized target function. We derive the L1 and L2 convergence rates of the estimator and prove the variable selection consistency. We further establish the asymptotic normality of any subset of the parameters, where the subset can have infinitely many components as long as its cardinality grows sufficiently slow. We develop Wald and score tests based on the asymptotic normality of the estimator, which permits testing of linear functions of the members if the subset. We examine the finite sample performance of the proposed tests by extensive simulation. Finally, the proposed method is successfully applied to the Alzheimer's Disease Neuroimaging Initiative study, which motivated this work initially.","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":null,"pages":null},"PeriodicalIF":4.5,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45193479","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: 1

BATCH POLICY LEARNING IN AVERAGE REWARD MARKOV DECISION PROCESSES. 平均奖励马尔可夫决策过程中的批量策略学习。

IF 4.5 1区数学

Annals of Statistics Pub Date : 2022-12-01 DOI: 10.1214/22-aos2231

Peng Liao, Zhengling Qi, Runzhe Wan, Predrag Klasnja, Susan A Murphy

引用次数: 55

LINEAR BIOMARKER COMBINATION FOR CONSTRAINED CLASSIFICATION. 约束分类的线性生物标志物组合。

IF 4.5 1区数学

Annals of Statistics Pub Date : 2022-10-01 Epub Date: 2022-10-27 DOI: 10.1214/22-aos2210

Yijian Huang, Martin G Sanda

{"title":"LINEAR BIOMARKER COMBINATION FOR CONSTRAINED CLASSIFICATION.","authors":"Yijian Huang, Martin G Sanda","doi":"10.1214/22-aos2210","DOIUrl":"https://doi.org/10.1214/22-aos2210","url":null,"abstract":"Multiple biomarkers are often combined to improve disease diagnosis. The uniformly optimal combination, i.e., with respect to all reasonable performance metrics, unfortunately requires excessive distributional modeling, to which the estimation can be sensitive. An alternative strategy is rather to pursue local optimality with respect to a specific performance metric. Nevertheless, existing methods may not target clinical utility of the intended medical test, which usually needs to operate above a certain sensitivity or specificity level, or do not have their statistical properties well studied and understood. In this article, we develop and investigate a linear combination method to maximize the clinical utility empirically for such a constrained classification. The combination coefficient is shown to have cube root asymptotics. The convergence rate and limiting distribution of the predictive performance are subsequently established, exhibiting robustness of the method in comparison with others. An algorithm with sound statistical justification is devised for efficient and high-quality computation. Simulations corroborate the theoretical results, and demonstrate good statistical and computational performance. Illustration with a clinical study on aggressive prostate cancer detection is provided.","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":null,"pages":null},"PeriodicalIF":4.5,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9635489/pdf/nihms-1819429.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40449706","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: 1

DOUBLY DEBIASED LASSO: HIGH-DIMENSIONAL INFERENCE UNDER HIDDEN CONFOUNDING. 双重去偏套索:隐藏混杂下的高维推理。

IF 4.5 1区数学

Annals of Statistics Pub Date : 2022-06-01 Epub Date: 2022-06-16 DOI: 10.1214/21-aos2152

Zijian Guo, Domagoj Ćevid, Peter Bühlmann

引用次数: 23

SURPRISES IN HIGH-DIMENSIONAL RIDGELESS LEAST SQUARES INTERPOLATION. 高维无脊最小二乘插值中的奇异值。

IF 4.5 1区数学

Annals of Statistics Pub Date : 2022-04-01 Epub Date: 2022-04-07 DOI: 10.1214/21-aos2133

Trevor Hastie, Andrea Montanari, Saharon Rosset, Ryan J Tibshirani

{"title":"SURPRISES IN HIGH-DIMENSIONAL RIDGELESS LEAST SQUARES INTERPOLATION.","authors":"Trevor Hastie, Andrea Montanari, Saharon Rosset, Ryan J Tibshirani","doi":"10.1214/21-aos2133","DOIUrl":"https://doi.org/10.1214/21-aos2133","url":null,"abstract":"Interpolators-estimators that achieve zero training error-have attracted growing attention in machine learning, mainly because state-of-the art neural networks appear to be models of this type. In this paper, we study minimum ℓ 2 norm (\"ridgeless\") interpolation least squares regression, focusing on the high-dimensional regime in which the number of unknown parameters p is of the same order as the number of samples n. We consider two different models for the feature distribution: a linear model, where the feature vectors <math> <mrow><msub><mi>x</mi> <mi>i</mi></msub> <mo>∈</mo> <msup><mi>ℝ</mi> <mi>p</mi></msup> </mrow> </math> are obtained by applying a linear transform to a vector of i.i.d. entries, x i = Σ1/2 z i (with <math> <mrow><msub><mi>z</mi> <mi>i</mi></msub> <mo>∈</mo> <msup><mi>ℝ</mi> <mi>p</mi></msup> </mrow> </math> ); and a nonlinear model, where the feature vectors are obtained by passing the input through a random one-layer neural network, xi = φ(Wz i ) (with <math> <mrow><msub><mi>z</mi> <mi>i</mi></msub> <mo>∈</mo> <msup><mi>ℝ</mi> <mi>d</mi></msup> </mrow> </math> , <math><mrow><mi>W</mi> <mo>∈</mo> <msup><mi>ℝ</mi> <mrow><mi>p</mi> <mo>×</mo> <mi>d</mi></mrow> </msup> </mrow> </math> a matrix of i.i.d. entries, and φ an activation function acting componentwise on Wz i ). We recover-in a precise quantitative way-several phenomena that have been observed in large-scale neural networks and kernel machines, including the \"double descent\" behavior of the prediction risk, and the potential benefits of overparametrization.","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":null,"pages":null},"PeriodicalIF":4.5,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9481183/pdf/nihms-1830540.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40367700","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: 579

OPTIMAL FALSE DISCOVERY RATE CONTROL FOR LARGE SCALE MULTIPLE TESTING WITH AUXILIARY INFORMATION. 基于辅助信息的大规模多重测试的最优错误发现率控制。

IF 4.5 1区数学

Annals of Statistics Pub Date : 2022-04-01 DOI: 10.1214/21-aos2128

Hongyuan Cao, Jun Chen, Xianyang Zhang

{"title":"OPTIMAL FALSE DISCOVERY RATE CONTROL FOR LARGE SCALE MULTIPLE TESTING WITH AUXILIARY INFORMATION.","authors":"Hongyuan Cao, Jun Chen, Xianyang Zhang","doi":"10.1214/21-aos2128","DOIUrl":"https://doi.org/10.1214/21-aos2128","url":null,"abstract":"Large-scale multiple testing is a fundamental problem in high dimensional statistical inference. It is increasingly common that various types of auxiliary information, reflecting the structural relationship among the hypotheses, are available. Exploiting such auxiliary information can boost statistical power. To this end, we propose a framework based on a two-group mixture model with varying probabilities of being null for different hypotheses a priori, where a shape-constrained relationship is imposed between the auxiliary information and the prior probabilities of being null. An optimal rejection rule is designed to maximize the expected number of true positives when average false discovery rate is controlled. Focusing on the ordered structure, we develop a robust EM algorithm to estimate the prior probabilities of being null and the distribution of p-values under the alternative hypothesis simultaneously. We show that the proposed method has better power than state-of-the-art competitors while controlling the false discovery rate, both empirically and theoretically. Extensive simulations demonstrate the advantage of the proposed method. Datasets from genome-wide association studies are used to illustrate the new methodology.","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":null,"pages":null},"PeriodicalIF":4.5,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10153594/pdf/nihms-1840915.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9776938","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: 15

Testability of high-dimensional linear models with nonsparse structures. 非稀疏结构高维线性模型的可测试性。

IF 4.5 1区数学

Annals of Statistics Pub Date : 2022-04-01 Epub Date: 2022-04-07 DOI: 10.1214/19-aos1932

Jelena Bradic, Jianqing Fan, Yinchu Zhu

{"title":"Testability of high-dimensional linear models with nonsparse structures.","authors":"Jelena Bradic, Jianqing Fan, Yinchu Zhu","doi":"10.1214/19-aos1932","DOIUrl":"https://doi.org/10.1214/19-aos1932","url":null,"abstract":"Understanding statistical inference under possibly non-sparse high-dimensional models has gained much interest recently. For a given component of the regression coefficient, we show that the difficulty of the problem depends on the sparsity of the corresponding row of the precision matrix of the covariates, not the sparsity of the regression coefficients. We develop new concepts of uniform and essentially uniform non-testability that allow the study of limitations of tests across a broad set of alternatives. Uniform non-testability identifies a collection of alternatives such that the power of any test, against any alternative in the group, is asymptotically at most equal to the nominal size. Implications of the new constructions include new minimax testability results that, in sharp contrast to the current results, do not depend on the sparsity of the regression parameters. We identify new tradeoffs between testability and feature correlation. In particular, we show that, in models with weak feature correlations, minimax lower bound can be attained by a test whose power has the <math> <mrow><msqrt><mi>n</mi></msqrt> </mrow> </math> rate, regardless of the size of the model sparsity.","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":null,"pages":null},"PeriodicalIF":4.5,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9266975/pdf/nihms-1639563.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40580296","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: 11