Annals of Statistics最新文献_第4页

FUNCTIONAL SUFFICIENT DIMENSION REDUCTION THROUGH AVERAGE FRÉCHET DERIVATIVES. 通过平均弗雷谢特导数实现函数充分降维。

IF 4.5 1区数学

Annals of Statistics Pub Date : 2022-04-01 Epub Date: 2022-04-07 DOI: 10.1214/21-aos2131

Kuang-Yao Lee, Lexin Li

{"title":"FUNCTIONAL SUFFICIENT DIMENSION REDUCTION THROUGH AVERAGE FRÉCHET DERIVATIVES.","authors":"Kuang-Yao Lee, Lexin Li","doi":"10.1214/21-aos2131","DOIUrl":"10.1214/21-aos2131","url":null,"abstract":"Sufficient dimension reduction (SDR) embodies a family of methods that aim for reduction of dimensionality without loss of information in a regression setting. In this article, we propose a new method for nonparametric function-on-function SDR, where both the response and the predictor are a function. We first develop the notions of functional central mean subspace and functional central subspace, which form the population targets of our functional SDR. We then introduce an average Fréchet derivative estimator, which extends the gradient of the regression function to the operator level and enables us to develop estimators for our functional dimension reduction spaces. We show the resulting functional SDR estimators are unbiased and exhaustive, and more importantly, without imposing any distributional assumptions such as the linearity or the constant variance conditions that are commonly imposed by all existing functional SDR methods. We establish the uniform convergence of the estimators for the functional dimension reduction spaces, while allowing both the number of Karhunen-Loève expansions and the intrinsic dimension to diverge with the sample size. We demonstrate the efficacy of the proposed methods through both simulations and two real data examples.","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/PMC10085580/pdf/nihms-1746366.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9320340","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

Spatial dependence and space–time trend in extreme events 极端事件的空间依赖性和时空趋势

IF 4.5 1区数学

Annals of Statistics Pub Date : 2022-02-01 DOI: 10.1214/21-aos2067

John H. J. Einmahl,Ana Ferreira,Laurens de Haan,Cláudia Neves,Chen Zhou

引用次数: 0

SEMIPARAMETRIC LATENT-CLASS MODELS FOR MULTIVARIATE LONGITUDINAL AND SURVIVAL DATA. 多变量纵向和生存数据的半参数潜伏类模型。

IF 4.5 1区数学

Annals of Statistics Pub Date : 2022-02-01 Epub Date: 2022-02-16 DOI: 10.1214/21-aos2117

Kin Yau Wong, Donglin Zeng, D Y Lin

引用次数: 0

CANONICAL THRESHOLDING FOR NON-SPARSE HIGH-DIMENSIONAL LINEAR REGRESSION. 非稀疏高维线性回归的典型阈值。

IF 4.5 1区数学

Annals of Statistics Pub Date : 2022-02-01 Epub Date: 2022-02-16 DOI: 10.1214/21-aos2116

Igor Silin, Jianqing Fan

{"title":"CANONICAL THRESHOLDING FOR NON-SPARSE HIGH-DIMENSIONAL LINEAR REGRESSION.","authors":"Igor Silin, Jianqing Fan","doi":"10.1214/21-aos2116","DOIUrl":"https://doi.org/10.1214/21-aos2116","url":null,"abstract":"We consider a high-dimensional linear regression problem. Unlike many papers on the topic, we do not require sparsity of the regression coefficients; instead, our main structural assumption is a decay of eigenvalues of the covariance matrix of the data. We propose a new family of estimators, called the canonical thresholding estimators, which pick largest regression coefficients in the canonical form. The estimators admit an explicit form and can be linked to LASSO and Principal Component Regression (PCR). A theoretical analysis for both fixed design and random design settings is provided. Obtained bounds on the mean squared error and the prediction error of a specific estimator from the family allow to clearly state sufficient conditions on the decay of eigenvalues to ensure convergence. In addition, we promote the use of the relative errors, strongly linked with the out-of-sample R 2. The study of these relative errors leads to a new concept of joint effective dimension, which incorporates the covariance of the data and the regression coefficients simultaneously, and describes the complexity of a linear regression problem. Some minimax lower bounds are established to showcase the optimality of our procedure. Numerical simulations confirm good performance of the proposed estimators compared to the previously developed methods.","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":null,"pages":null},"PeriodicalIF":4.5,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9491498/pdf/nihms-1782574.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"33478241","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: 2

Total variation regularized Fréchet regression for metric-space valued data 度量空间值数据的总变分正则化fr<s:1>回归

IF 4.5 1区数学

Annals of Statistics Pub Date : 2021-12-01 DOI: 10.1214/21-aos2095

Zhenhua Lin,Hans-Georg Müller

{"title":"Total variation regularized Fréchet regression for metric-space valued data","authors":"Zhenhua Lin,Hans-Georg Müller","doi":"10.1214/21-aos2095","DOIUrl":"https://doi.org/10.1214/21-aos2095","url":null,"abstract":"Non-Euclidean data that are indexed with a scalar predictor such as time are increasingly encountered in data applications, while statistical methodology and theory for such random objects are not well developed yet. To address the need for new methodology in this area, we develop a total variation regularization technique for nonparametric Frechet regression, which refers to a regression setting where a response residing in a generic metric space is paired with a scalar predictor and the target is a conditional Frechet mean. Specifically, we seek to approximate an unknown metric-space valued function by an estimator that minimizes the Frechet version of least squares and at the same time has small total variation, appropriately defined for metric-space valued objects. We show that the resulting estimator is representable by a piece-wise constant function and establish the minimax convergence rate of the proposed estimator for metric data objects that reside in Hadamard spaces. We illustrate the numerical performance of the proposed method for both simulated and real data, including metric spaces of symmetric positive-definite matrices with the affine-invariant distance, of probability distributions on the real line with the Wasserstein distance, and of phylogenetic trees with the Billera--Holmes--Vogtmann metric.","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":null,"pages":null},"PeriodicalIF":4.5,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138508224","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: 13

BRIDGING CONVEX AND NONCONVEX OPTIMIZATION IN ROBUST PCA: NOISE, OUTLIERS, AND MISSING DATA. 在鲁棒 PCA 中连接凸优化和非凸优化：噪声、异常值和缺失数据。

IF 3.2 1区数学

Annals of Statistics Pub Date : 2021-10-01 Epub Date: 2021-11-12 DOI: 10.1214/21-aos2066

Yuxin Chen, Jianqing Fan, Cong Ma, Yuling Yan

引用次数: 0

BOOSTED NONPARAMETRIC HAZARDS WITH TIME-DEPENDENT COVARIATES. 具有时间相关协变量的增强非参数风险。

IF 4.5 1区数学

Annals of Statistics Pub Date : 2021-08-01 Epub Date: 2021-09-29 DOI: 10.1214/20-aos2028

Donald K K Lee, Ningyuan Chen, Hemant Ishwaran

引用次数: 0

ASYMPTOTIC DISTRIBUTIONS OF HIGH-DIMENSIONAL DISTANCE CORRELATION INFERENCE. 高维距离相关推断的渐近分布。

IF 4.5 1区数学

Annals of Statistics Pub Date : 2021-08-01 Epub Date: 2021-09-29 DOI: 10.1214/20-aos2024

Lan Gao, Yingying Fan, Jinchi Lv, Qi-Man Shao

{"title":"ASYMPTOTIC DISTRIBUTIONS OF HIGH-DIMENSIONAL DISTANCE CORRELATION INFERENCE.","authors":"Lan Gao, Yingying Fan, Jinchi Lv, Qi-Man Shao","doi":"10.1214/20-aos2024","DOIUrl":"10.1214/20-aos2024","url":null,"abstract":"Distance correlation has become an increasingly popular tool for detecting the nonlinear dependence between a pair of potentially high-dimensional random vectors. Most existing works have explored its asymptotic distributions under the null hypothesis of independence between the two random vectors when only the sample size or the dimensionality diverges. Yet its asymptotic null distribution for the more realistic setting when both sample size and dimensionality diverge in the full range remains largely underdeveloped. In this paper, we fill such a gap and develop central limit theorems and associated rates of convergence for a rescaled test statistic based on the bias-corrected distance correlation in high dimensions under some mild regularity conditions and the null hypothesis. Our new theoretical results reveal an interesting phenomenon of blessing of dimensionality for high-dimensional distance correlation inference in the sense that the accuracy of normal approximation can increase with dimensionality. Moreover, we provide a general theory on the power analysis under the alternative hypothesis of dependence, and further justify the capability of the rescaled distance correlation in capturing the pure nonlinear dependency under moderately high dimensionality for a certain type of alternative hypothesis. The theoretical results and finite-sample performance of the rescaled statistic are illustrated with several simulation examples and a blockchain application.","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":null,"pages":null},"PeriodicalIF":4.5,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8491772/pdf/nihms-1684707.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39495519","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 SHRINKAGE PRINCIPLE FOR HEAVY-TAILED DATA: HIGH-DIMENSIONAL ROBUST LOW-RANK MATRIX RECOVERY. 重尾数据的收缩原理：高维稳健低秩矩阵恢复。

IF 4.5 1区数学

Annals of Statistics Pub Date : 2021-06-01 Epub Date: 2021-08-09 DOI: 10.1214/20-aos1980

Jianqing Fan, Weichen Wang, Ziwei Zhu

{"title":"A SHRINKAGE PRINCIPLE FOR HEAVY-TAILED DATA: HIGH-DIMENSIONAL ROBUST LOW-RANK MATRIX RECOVERY.","authors":"Jianqing Fan, Weichen Wang, Ziwei Zhu","doi":"10.1214/20-aos1980","DOIUrl":"10.1214/20-aos1980","url":null,"abstract":"This paper introduces a simple principle for robust statistical inference via appropriate shrinkage on the data. This widens the scope of high-dimensional techniques, reducing the distributional conditions from sub-exponential or sub-Gaussian to more relaxed bounded second or fourth moment. As an illustration of this principle, we focus on robust estimation of the low-rank matrix Θ* from the trace regression model Y = Tr(Θ*⊤ X) + ϵ. It encompasses four popular problems: sparse linear model, compressed sensing, matrix completion and multi-task learning. We propose to apply the penalized least-squares approach to the appropriately truncated or shrunk data. Under only bounded 2+δ moment condition on the response, the proposed robust methodology yields an estimator that possesses the same statistical error rates as previous literature with sub-Gaussian errors. For sparse linear model and multi-task regression, we further allow the design to have only bounded fourth moment and obtain the same statistical rates. As a byproduct, we give a robust covariance estimator with concentration inequality and optimal rate of convergence in terms of the spectral norm, when the samples only bear bounded fourth moment. This result is of its own interest and importance. We reveal that under high dimensions, the sample covariance matrix is not optimal whereas our proposed robust covariance can achieve optimality. Extensive simulations are carried out to support the theories.","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":null,"pages":null},"PeriodicalIF":4.5,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8457508/pdf/nihms-1639579.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39443652","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: 69

Survival analysis via hierarchically dependent mixture hazards 通过分级依赖混合物危害进行生存分析

IF 4.5 1区数学

Annals of Statistics Pub Date : 2021-04-01 DOI: 10.1214/20-AOS1982

F. Camerlenghi, A. Lijoi, I. Pruenster

{"title":"Survival analysis via hierarchically dependent mixture hazards","authors":"F. Camerlenghi, A. Lijoi, I. Pruenster","doi":"10.1214/20-AOS1982","DOIUrl":"https://doi.org/10.1214/20-AOS1982","url":null,"abstract":"Hierarchical nonparametric processes are popular tools for defining priors on collections of probability distributions, which induce dependence across multiple samples. In survival analysis problems one is typically interested in modeling the hazard rates, rather than the probability distributions themselves, and the currently available methodologies are not applicable. Here we fill this gap by introducing a novel, and analytically tractable, class of multivariate mixtures whose distribution acts as a prior for the vector of sample–specific baseline hazard rates. The dependence is induced through a hierarchical specification for the mixing random measures that ultimately corresponds to a composition of random discrete combinatorial structures. Our theoretical results allow to develop a full Bayesian analysis for this class of models, which can also account for right–censored survival data and covariates, and we also show posterior consistency. In particular, we emphasize that the posterior characterization we achieve is the key for devising both marginal and conditional algorithms for evaluating Bayesian inferences of interest. The effectiveness of our proposal is illustrated through some synthetic and real data examples.","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":null,"pages":null},"PeriodicalIF":4.5,"publicationDate":"2021-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49201957","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: 11