Annals of Statistics最新文献_第8页

A UNIFIED STUDY OF NONPARAMETRIC INFERENCE FOR MONOTONE FUNCTIONS. 单调函数非参数推断的统一研究。

IF 4.5 1区数学

Annals of Statistics Pub Date : 2020-04-01 Epub Date: 2020-05-26 DOI: 10.1214/19-aos1835

Ted Westling, Marco Carone

{"title":"A UNIFIED STUDY OF NONPARAMETRIC INFERENCE FOR MONOTONE FUNCTIONS.","authors":"Ted Westling, Marco Carone","doi":"10.1214/19-aos1835","DOIUrl":"10.1214/19-aos1835","url":null,"abstract":"<p><p>The problem of nonparametric inference on a monotone function has been extensively studied in many particular cases. Estimators considered have often been of so-called Grenander type, being representable as the left derivative of the greatest convex minorant or least concave majorant of an estimator of a primitive function. In this paper, we provide general conditions for consistency and pointwise convergence in distribution of a class of generalized Grenander-type estimators of a monotone function. This broad class allows the minorization or majoratization operation to be performed on a data-dependent transformation of the domain, possibly yielding benefits in practice. Additionally, we provide simpler conditions and more concrete distributional theory in the important case that the primitive estimator and data-dependent transformation function are asymptotically linear. We use our general results in the context of various well-studied problems, and show that we readily recover classical results established separately in each case. More importantly, we show that our results allow us to tackle more challenging problems involving parameters for which the use of flexible learning strategies appears necessary. In particular, we study inference on monotone density and hazard functions using informatively right-censored data, extending the classical work on independent censoring, and on a covariate-marginalized conditional mean function, extending the classical work on monotone regression functions.</p>","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":null,"pages":null},"PeriodicalIF":4.5,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7377427/pdf/nihms-1597646.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38194372","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

Inference for Archimax copulas 阿基米德交配式的推论

IF 4.5 1区数学

Annals of Statistics Pub Date : 2020-04-01 DOI: 10.1214/19-aos1836

Simon Chatelain, Anne-Laure Fougères, J. Nešlehová

{"title":"Inference for Archimax copulas","authors":"Simon Chatelain, Anne-Laure Fougères, J. Nešlehová","doi":"10.1214/19-aos1836","DOIUrl":"https://doi.org/10.1214/19-aos1836","url":null,"abstract":"Archimax copula models can account for any type of asymptotic dependence between extremes and at the same time capture joint risks at medium levels. An Archimax copula is characterized by two functional parameters, the stable tail dependence function `, and the Archimedean generator ψ which distorts the extreme-value dependence structure. This article develops semiparametric inference for Archimax copulas: a nonparametric estimator of ` and a momentbased estimator of ψ assuming the latter belongs to a parametric family. Conditions under which ψ and ` are identifiable are derived. The asymptotic behavior of the estimators is then established under broad regularity conditions; performance in small samples is assessed through a comprehensive simulation study. The Archimax copula model with the Clayton generator is then used to analyze monthly rainfall maxima at three stations in French Brittany. The model is seen to fit the data very well, both in the lower and in the upper tail. The nonparametric estimator of ` reveals asymmetric extremal dependence between the stations, which reflects heavy precipitation patterns in the area. Technical proofs, simulation results and R code are provided in the Online Supplement.","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":null,"pages":null},"PeriodicalIF":4.5,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44067400","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: 9

Hurst function estimation 赫斯特函数估计

IF 4.5 1区数学

Annals of Statistics Pub Date : 2020-04-01 DOI: 10.1214/19-aos1825

Jinqi Shen, T. Hsing

引用次数: 1

Worst-case versus average-case design for estimation from partial pairwise comparisons 根据部分成对比较进行估计的最坏情况与平均情况设计

IF 4.5 1区数学

Annals of Statistics Pub Date : 2020-04-01 DOI: 10.1214/19-aos1838

A. Pananjady, Cheng Mao, Vidya Muthukumar, M. Wainwright, T. Courtade

{"title":"Worst-case versus average-case design for estimation from partial pairwise comparisons","authors":"A. Pananjady, Cheng Mao, Vidya Muthukumar, M. Wainwright, T. Courtade","doi":"10.1214/19-aos1838","DOIUrl":"https://doi.org/10.1214/19-aos1838","url":null,"abstract":"Pairwise comparison data arises in many domains, including tournament rankings, web search, and preference elicitation. Given noisy comparisons of a fixed subset of pairs of items, we study the problem of estimating the underlying comparison probabilities under the assumption of strong stochastic transitivity (SST). We also consider the noisy sorting subclass of the SST model. We show that when the assignment of items to the topology is arbitrary, these permutationbased models, unlike their parametric counterparts, do not admit consistent estimation for most comparison topologies used in practice. We then demonstrate that consistent estimation is possible when the assignment of items to the topology is randomized, thus establishing a dichotomy between worst-case and average-case designs. We propose two computationally efficient estimators in the average-case setting and analyze their risk, showing that it depends on the comparison topology only through the degree sequence of the topology. We also provide explicit classes of graphs for which the rates achieved by these estimators are optimal. Our results are corroborated by simulations on multiple comparison topologies.","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":null,"pages":null},"PeriodicalIF":4.5,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49323852","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: 9

Prediction error after model search 模型搜索后的预测错误

IF 4.5 1区数学

Annals of Statistics Pub Date : 2020-04-01 DOI: 10.1214/19-AOS1818

Xiaoying Tian

引用次数: 16

Bootstrap confidence regions based on M-estimators under nonstandard conditions 非标准条件下基于m估计量的自举置信区域

IF 4.5 1区数学

Annals of Statistics Pub Date : 2020-02-01 DOI: 10.1214/18-aos1803

Stephen M. S. Lee, Puyudi Yang

引用次数: 5

Two-step semiparametric empirical likelihood inference 两步半参数经验似然推理

IF 4.5 1区数学

Annals of Statistics Pub Date : 2020-02-01 DOI: 10.1214/18-AOS1788

Francesco Bravo, J. Escanciano, I. Keilegom

引用次数: 19

The multi-armed bandit problem: An efficient nonparametric solution 多武装土匪问题：一个有效的非参数解

IF 4.5 1区数学

Annals of Statistics Pub Date : 2020-02-01 DOI: 10.1214/19-aos1809

H. Chan

引用次数: 13

Sparse SIR: Optimal rates and adaptive estimation 稀疏SIR:最优速率和自适应估计

IF 4.5 1区数学

Annals of Statistics Pub Date : 2020-02-01 DOI: 10.1214/18-aos1791

Kai Tan, Lei Shi, Zhou Yu

引用次数: 17

Penalized generalized empirical likelihood with a diverging number of general estimating equations for censored data 截尾数据广义估计方程具有发散数的惩罚广义经验似然

IF 4.5 1区数学

Annals of Statistics Pub Date : 2020-02-01 DOI: 10.1214/19-aos1870

Nian-Sheng Tang, Xiaodong Yan, Xingqiu Zhao

{"title":"Penalized generalized empirical likelihood with a diverging number of general estimating equations for censored data","authors":"Nian-Sheng Tang, Xiaodong Yan, Xingqiu Zhao","doi":"10.1214/19-aos1870","DOIUrl":"https://doi.org/10.1214/19-aos1870","url":null,"abstract":"This article considers simultaneous variable selection and parameter estimation as well as hypothesis testing in censored regression models with unspecified parametric likelihood. For the problem, we utilize certain growing dimensional general estimating equations and propose a penalized generalized empirical likelihood using the folded concave penalties. We first construct general estimating equations attaining the semiparametric efficiency bound with censored regression data and then establish the consistency and oracle properties of the penalized generalized empirical likelihood estimators. Furthermore, we show that the penalized generalized empirical likelihood ratio test statistic has an asymptotic standard central chi-squared distribution. The conditions of local and restricted global optimality of weighted penalized generalized empirical likelihood estimators are also discussed. We present an two-layer iterative algorithm for efficient implementation, and rigorously investigate its convergence property. The good performance of the proposed methods are demonstrated by extensive simulation studies and a real data example is provided for illustration.","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":null,"pages":null},"PeriodicalIF":4.5,"publicationDate":"2020-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44061735","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: 3