The Annals of Statistics最新文献_第7页

Optimal difference-based variance estimators in time series: A general framework 时间序列中基于差分的最优方差估计:一般框架

The Annals of Statistics Pub Date : 2021-12-30 DOI: 10.1214/21-aos2154

Kin Wai Chan

引用次数: 7

Total positivity in multivariate extremes 多元极值中的总正性

The Annals of Statistics Pub Date : 2021-12-29 DOI: 10.1214/23-aos2272

Frank Rottger, Sebastian Engelke, Piotr Zwiernik

{"title":"Total positivity in multivariate extremes","authors":"Frank Rottger, Sebastian Engelke, Piotr Zwiernik","doi":"10.1214/23-aos2272","DOIUrl":"https://doi.org/10.1214/23-aos2272","url":null,"abstract":"Positive dependence is present in many real world data sets and has appealing stochastic properties that can be exploited in statistical modeling and in estimation. In particular, the notion of multivariate total positivity of order 2 ($ mathrm{MTP}_{2} $) is a convex constraint and acts as an implicit regularizer in the Gaussian case. We study positive dependence in multivariate extremes and introduce $ mathrm{EMTP}_{2} $, an extremal version of $ mathrm{MTP}_{2} $. This notion turns out to appear prominently in extremes, and in fact, it is satisfied by many classical models. For a H\"usler--Reiss distribution, the analogue of a Gaussian distribution in extremes, we show that it is $ mathrm{EMTP}_{2} $ if and only if its precision matrix is a Laplacian of a connected graph. We propose an estimator for the parameters of the H\"usler--Reiss distribution under $ mathrm{EMTP}_{2} $ as the solution of a convex optimization problem with Laplacian constraint. We prove that this estimator is consistent and typically yields a sparse model with possibly nondecomposable extremal graphical structure. Applying our methods to a data set of Danube River flows, we illustrate this regularization and the superior performance compared to existing methods.","PeriodicalId":22375,"journal":{"name":"The Annals of Statistics","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82875264","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: 14

Local permutation tests for conditional independence 条件独立性的局部排列检验

The Annals of Statistics Pub Date : 2021-12-22 DOI: 10.1214/22-aos2233

Ilmun Kim, Matey Neykov, Sivaraman Balakrishnan, L. Wasserman

{"title":"Local permutation tests for conditional independence","authors":"Ilmun Kim, Matey Neykov, Sivaraman Balakrishnan, L. Wasserman","doi":"10.1214/22-aos2233","DOIUrl":"https://doi.org/10.1214/22-aos2233","url":null,"abstract":"In this paper, we investigate local permutation tests for testing conditional independence between two random vectors X and Y given Z . The local permutation test determines the signiﬁcance of a test statistic by locally shufﬂing samples which share similar values of the conditioning variables Z , and it forms a natural extension of the usual permutation approach for unconditional independence testing. Despite its simplicity and empirical support, the theoretical underpinnings of the local permutation test remain unclear. Motivated by this gap, this paper aims to establish theoretical foundations of local permutation tests with a particular focus on binning-based statistics. We start by revisiting the hardness of conditional independence testing and provide an upper bound for the power of any valid conditional independence test, which holds when the probability of observing “collisions” in Z is small. This negative result naturally motivates us to impose additional restrictions on the possible distributions under the null and alternate. To this end, we focus our attention on certain classes of smooth distributions and identify provably tight conditions under which the local permutation method is universally valid, i.e. it is valid when applied to any (binning-based) test statistic. To complement this result on type I error control, we also show that in some cases, a binning-based statistic calibrated via the local permutation method can achieve minimax optimal power. We also introduce a double-binning permutation strategy, which yields a valid test over less smooth null distributions than the typical single-binning method without compromising much power. Finally, we present simulation results to support our theoretical","PeriodicalId":22375,"journal":{"name":"The Annals of Statistics","volume":"62 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85565845","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: 13

The integrated copula spectrum 积分共轭谱

The Annals of Statistics Pub Date : 2021-12-14 DOI: 10.1214/22-AOS2240

Yuichi Goto, Tobias Kley, Ria Van Hecke, S. Volgushev, H. Dette, M. Hallin

{"title":"The integrated copula spectrum","authors":"Yuichi Goto, Tobias Kley, Ria Van Hecke, S. Volgushev, H. Dette, M. Hallin","doi":"10.1214/22-AOS2240","DOIUrl":"https://doi.org/10.1214/22-AOS2240","url":null,"abstract":"Frequency domain methods form a ubiquitous part of the statistical tool-box for time series analysis. In recent years, considerable interest has been given to the development of new spectral methodology and tools capturing dynamics in the entire joint distributions and thus avoiding the limitations of classical, L 2 -based spectral methods. Most of the spectral concepts proposed in that literature suffer from one major drawback, though: their estimation re-quires the choice of a smoothing parameter, which has a considerable impact on estimation quality and poses challenges for statistical inference. In this paper, associated with the concept of copula-based spectrum, we introduce the notion of copula spectral distribution function or integrated copula spectrum . This integrated copula spectrum retains the advantages of copula-based spectra but can be estimated without the need for smoothing parameters. We provide such estimators, along with a thorough theoretical analysis, based on a functional central limit theorem, of their asymptotic properties. We leverage these results to test various hypotheses that cannot be addressed by classical spectral methods, such as the lack of time-reversibility or asymmetry in tail dynamics.","PeriodicalId":22375,"journal":{"name":"The Annals of Statistics","volume":"38 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76479775","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: 0

Analysis of generalized Bregman surrogate algorithms for nonsmooth nonconvex statistical learning 非光滑非凸统计学习的广义Bregman代理算法分析

The Annals of Statistics Pub Date : 2021-12-01 DOI: 10.1214/21-aos2090

Yiyuan She, Zhifeng Wang, Jiuwu Jin

引用次数: 7

On fixed-domain asymptotics, parameter estimation and isotropic Gaussian random fields with Matérn covariance functions 关于固定域渐近性、参数估计和各向同性高斯随机场的mat<s:1>协方差函数

The Annals of Statistics Pub Date : 2021-12-01 DOI: 10.1214/21-aos2077

Wei-Liem Loh, Saifei Sun, J. Wen

引用次数: 2

Optimal linear discriminators for the discrete choice model in growing dimensions 增长维数下离散选择模型的最优线性判别器

The Annals of Statistics Pub Date : 2021-12-01 DOI: 10.1214/21-aos2085

Debarghya Mukherjee, M. Banerjee

引用次数: 4

Posterior analysis of n in the binomial (n,p) problem with both parameters unknown—with applications to quantitative nanoscopy 两个参数都未知的二项(n,p)问题中n的后验分析-应用于定量纳米显微镜

The Annals of Statistics Pub Date : 2021-12-01 DOI: 10.1214/21-aos2096

Johannes Schmidt-Hieber, Laura Fee Schneider, Thomas Staudt, A. Krajina, Timo Aspelmeier, Axel Munk

引用次数: 1

Rate-optimal cluster-randomized designs for spatial interference 空间干扰率最优聚类随机设计

The Annals of Statistics Pub Date : 2021-11-08 DOI: 10.1214/22-aos2224

Michael P. Leung

{"title":"Rate-optimal cluster-randomized designs for spatial interference","authors":"Michael P. Leung","doi":"10.1214/22-aos2224","DOIUrl":"https://doi.org/10.1214/22-aos2224","url":null,"abstract":"We consider a potential outcomes model in which interference may be present between any two units but the extent of interference diminishes with spatial distance. The causal estimand is the global average treatment effect, which compares counterfactual outcomes when all units are treated to those when none are. We study a class of designs in which space is partitioned into clusters that are randomized into treatment and control. For each design, we estimate the treatment effect using a Horvitz-Thompson estimator that compares the average outcomes of units with all neighbors treated to units with no treated neighbors, where the neighborhood radius is of the same order as the cluster size dictated by the design. We derive the estimator’s rate of convergence as a function of the design and degree of interference and use this to obtain estimator-design pairs that achieve near-optimal rates of convergence under relatively minimal assumptions on interference. We prove that the estimators are asymptotically normal and provide a variance estimator. For practical implementation of the designs, we suggest partitioning space using clustering algorithms. only be directly observed in the data under an extreme design that assigns all units to the same treatment arm, which would necessarily preclude observation of the other counterfactual. Common designs used in the literature, including those studied here, assign different units to different treatment arms, so neither average is directly observed in the data. Nonetheless, we show that asymptotic inference on θ n is possible for a class of cluster-randomized designs under spatial interference where the degree of interference diminishes with distance.","PeriodicalId":22375,"journal":{"name":"The Annals of Statistics","volume":"60 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84708981","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: 11

On the disjoint and sliding block maxima method for piecewise stationary time series 分段平稳时间序列的不相交滑动块极大值法

The Annals of Statistics Pub Date : 2021-10-29 DOI: 10.1214/23-aos2260

Axel Bucher, L. Zanger

引用次数: 1