Annals of Statistics最新文献

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

IF 4.5 1区数学 Q1 STATISTICS & PROBABILITY

Annals of Statistics

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

Simon Chatelain, Anne-Laure Fougères, J. Nešlehová

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.

阿基米德copula模型可以解释极端之间的任何类型的渐近依赖性，同时捕捉中等水平的联合风险。阿基米德copula由两个函数参数表征，即稳定的尾部依赖函数和扭曲极值依赖结构的阿基米德生成器ψ。本文发展了阿基米德copula的半参数推断：`的非参数估计量和ψ的基于矩的估计量，假设后者属于参数族。导出了ψ和`可识别的条件。然后在广义正则性条件下建立了估计量的渐近行为；通过全面的模拟研究来评估小样本的性能。然后使用Clayton发电机的阿基米德copula模型来分析法属布列塔尼三个站点的月最大降雨量。该模型在下尾部和上尾部都很好地拟合了数据。`的非参数估计揭示了站点之间的非对称极值依赖性，反映了该地区的强降水模式。在线补充中提供了技术证明、模拟结果和R代码。

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引用次数: 9

Hurst function estimation 赫斯特函数估计

IF 4.5 1区数学 Q1 STATISTICS & PROBABILITY

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 Q1 STATISTICS & PROBABILITY

Annals of Statistics

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

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

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.

配对比较数据出现在许多领域，包括锦标赛排名、网络搜索和偏好启发。给定一个固定的项目对子集的噪声比较，我们研究了在强随机传递性（SST）假设下估计潜在比较概率的问题。我们还考虑SST模型的噪声排序子类。我们表明，当项目到拓扑的分配是任意的时，这些基于排列的模型与它们的参数对应模型不同，不允许对实践中使用的大多数比较拓扑进行一致的估计。然后，我们证明了当将项目分配到拓扑结构时，一致估计是可能的，从而在最坏情况和平均情况设计之间建立了二分法。我们在平均情况下提出了两个计算有效的估计量，并分析了它们的风险，表明它只通过拓扑的度序列依赖于比较拓扑。我们还提供了显式的图类，对于这些图类，由这些估计器实现的速率是最优的。我们的结果通过对多个比较拓扑的模拟得到了证实。

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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 Q1 STATISTICS & PROBABILITY

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 Q1 STATISTICS & PROBABILITY

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 Q1 STATISTICS & PROBABILITY

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 Q1 STATISTICS & PROBABILITY

Annals of Statistics

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

H. Chan

引用次数: 13

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 Q1 STATISTICS & PROBABILITY

Annals of Statistics

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

Nian-Sheng Tang, Xiaodong Yan, Xingqiu Zhao

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.

本文考虑了具有未指定参数似然的截尾回归模型中的变量选择和参数估计以及假设检验。对于这个问题，我们利用某些增长维的一般估计方程，并利用折叠凹罚分提出了一个罚分的广义经验似然。我们首先构造了获得截尾回归数据半参数有效界的一般估计方程，然后建立了惩罚广义经验似然估计的一致性和预言性。此外，我们证明了惩罚广义经验似然比检验统计量具有渐近标准中心卡方分布。讨论了加权惩罚广义经验似然估计的局部最优性和限制全局最优性的条件。我们提出了一种高效实现的两层迭代算法，并严格研究了其收敛性。通过大量的仿真研究证明了所提出的方法的良好性能，并提供了一个实际数据示例进行说明。

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引用次数: 3

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 Q1 STATISTICS & PROBABILITY

Annals of Statistics

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

Kai Tan, Lei Shi, Zhou Yu

Sliced inverse regression (SIR) is an innovative and effective method for sufficient dimension reduction and data visualization. Recently, an impressive range of penalized SIR methods has been proposed to estimate the central subspace in a sparse fashion. Nonetheless, few of them considered the sparse sufficient dimension reduction from a decision-theoretic point of view. To address this issue, we in this paper establish the minimax rates of convergence for estimating the sparse SIR directions under various commonly used loss functions in the literature of sufficient dimension reduction. We also discover the possible trade-off between statistical guarantee and computational performance for sparse SIR. We finally propose an adaptive estimation scheme for sparse SIR which is computationally tractable and rate optimal. Numerical studies are carried out to confirm the theoretical properties of our proposed methods.

切片逆回归(SIR)是实现充分降维和数据可视化的一种创新而有效的方法。最近，人们提出了一系列令人印象深刻的惩罚SIR方法，以稀疏方式估计中心子空间。然而，很少有人从决策理论的角度考虑稀疏充分降维问题。为了解决这一问题，本文建立了文献中各种常用损失函数在充分降维下估计稀疏SIR方向的极小极大收敛率。我们还发现了稀疏SIR的统计保证和计算性能之间可能存在的权衡。最后，我们提出了一种计算易于处理且速率最优的稀疏SIR自适应估计方案。数值研究证实了我们提出的方法的理论性质。

引用次数: 17

CONSISTENT SELECTION OF THE NUMBER OF CHANGE-POINTS VIA SAMPLE-SPLITTING. 通过样本分裂一致地选择改变点的数量。

IF 4.5 1区数学 Q1 STATISTICS & PROBABILITY

Annals of Statistics

Pub Date : 2020-02-01 Epub Date: 2020-02-17 DOI: 10.1214/19-aos1814

Changliang Zou, Guanghui Wang, Runze Li

In multiple change-point analysis, one of the major challenges is to estimate the number of change-points. Most existing approaches attempt to minimize a Schwarz information criterion which balances a term quantifying model fit with a penalization term accounting for model complexity that increases with the number of change-points and limits overfitting. However, different penalization terms are required to adapt to different contexts of multiple change-point problems and the optimal penalization magnitude usually varies from the model and error distribution. We propose a data-driven selection criterion that is applicable to most kinds of popular change-point detection methods, including binary segmentation and optimal partitioning algorithms. The key idea is to select the number of change-points that minimizes the squared prediction error, which measures the fit of a specified model for a new sample. We develop a cross-validation estimation scheme based on an order-preserved sample-splitting strategy, and establish its asymptotic selection consistency under some mild conditions. Effectiveness of the proposed selection criterion is demonstrated on a variety of numerical experiments and real-data examples.

在多变更点分析中，主要的挑战之一是估计变更点的数量。大多数现有的方法都试图最小化Schwarz信息准则，该准则平衡了一个量化模型拟合的项和一个考虑模型复杂性的惩罚项，模型复杂性随着变化点的数量和过度拟合的限制而增加。然而，多变点问题需要不同的惩罚项来适应不同的环境，最优的惩罚大小通常随模型和误差分布而变化。我们提出了一种数据驱动的选择准则，适用于大多数流行的变化点检测方法，包括二值分割和最优分割算法。关键思想是选择变化点的数量，使预测误差的平方最小化，这是对新样本的特定模型的拟合度量。我们提出了一种基于保持序的样本分割策略的交叉验证估计方案，并在一些温和条件下建立了它的渐近选择一致性。通过各种数值实验和实际数据算例验证了所提出的选择准则的有效性。

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引用次数: 28

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