Journal of the Royal Statistical Society Series B-Statistical Methodology最新文献

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Strategic two-sample test via the two-armed bandit process 通过双臂盗匪过程进行战略双样本检验

IF 5.8 1区数学 Q1 STATISTICS & PROBABILITY

Journal of the Royal Statistical Society Series B-Statistical Methodology

Pub Date : 2023-06-14 DOI: 10.1093/jrsssb/qkad061

Zengjing Chen, Xiaodong Yan, Guodong Zhang

This study aims to improve the power of two-sample tests by analysing whether the difference between two population parameters is larger than a prespecified positive equivalence margin. The classic test statistic treats the original data as exchangeable, while the proposed test statistic breaks the structure and proposes employing a two-armed bandit process to strategically integrate the data and thus a strategy-specific test statistic is constructed by combining the classic CLT with the law of large numbers. The developed asymptotic theory is investigated by using nonlinear limit theory in a larger probability space and relates to the ‘strategic CLT’ with a clearly defined density function. The asymptotic distribution demonstrates that the proposed statistic is more concentrated under the null hypothesis and less concentrated under the alternative than the classic CLT, thereby enhancing the testing power. Simulation studies provide supporting evidence for the theoretical results and portray a more powerful performance when using finite samples. A real example is also added for illustration.

本研究旨在通过分析两个总体参数之间的差异是否大于预先指定的正等效裕度来提高双样本检验的有效性。经典检验统计量将原始数据视为可交换的，而本文的检验统计量打破了这种结构，提出采用双臂强盗过程对数据进行策略整合，从而将经典的CLT与大数定律相结合，构建了针对策略的检验统计量。利用非线性极限理论在更大的概率空间中研究了渐近理论，该渐近理论涉及具有明确定义密度函数的“策略CLT”。渐近分布表明，与经典的CLT相比，所提出的统计量在零假设下更集中，在备选假设下更不集中，从而提高了检验能力。仿真研究为理论结果提供了支持证据，并在使用有限样本时描绘了更强大的性能。还添加了一个真实的例子来说明。

引用次数: 0

Quasi-Newton updating for large-scale distributed learning 大规模分布式学习的准牛顿更新

1区数学 Q1 STATISTICS & PROBABILITY

Journal of the Royal Statistical Society Series B-Statistical Methodology

Pub Date : 2023-06-10 DOI: 10.1093/jrsssb/qkad059

Shuyuan Wu, Danyang Huang, Hansheng Wang

Abstract Distributed computing is critically important for modern statistical analysis. Herein, we develop a distributed quasi-Newton (DQN) framework with excellent statistical, computation, and communication efficiency. In the DQN method, no Hessian matrix inversion or communication is needed. This considerably reduces the computation and communication complexity of the proposed method. Notably, related existing methods only analyse numerical convergence and require a diverging number of iterations to converge. However, we investigate the statistical properties of the DQN method and theoretically demonstrate that the resulting estimator is statistically efficient over a small number of iterations under mild conditions. Extensive numerical analyses demonstrate the finite sample performance.

分布式计算对现代统计分析至关重要。在此，我们开发了一个具有出色统计，计算和通信效率的分布式准牛顿(DQN)框架。在DQN方法中，不需要Hessian矩阵反演和通信。这大大降低了该方法的计算和通信复杂度。值得注意的是，现有的相关方法只分析数值收敛性，并且需要发散迭代数才能收敛。然而，我们研究了DQN方法的统计性质，并从理论上证明了在温和的条件下，在少量迭代中得到的估计器是统计有效的。大量的数值分析证明了有限样本的性能。

引用次数: 0

Correction to: Autoregressive optimal transport models. 更正：自回归最优运输模型。

IF 5.8 1区数学 Q1 STATISTICS & PROBABILITY

Journal of the Royal Statistical Society Series B-Statistical Methodology

Pub Date : 2023-05-31 eCollection Date: 2023-07-01 DOI: 10.1093/jrsssb/qkad057

[This corrects the article DOI: 10.1093/jrsssb/qkad051.].

[这更正了文章DOI:10.1093/jrsssb/qkad051.]。

引用次数: 0

Alexander Van Werde's contribution to the Discussion of ‘Vintage Factor Analysis with Varimax Performs Statistical Inference’ by Rohe & Zeng Alexander Van Werde对Rohe的“Vintage Factor Analysis with variimax perform Statistical Inference”讨论的贡献曾。

1区数学 Q1 STATISTICS & PROBABILITY

Journal of the Royal Statistical Society Series B-Statistical Methodology

Pub Date : 2023-05-25 DOI: 10.1093/jrsssb/qkad035

Alexander Van Werde

引用次数: 0

Konstantin Siroki and Korbinian Strimmer’s contribution to the Discussion of “Vintage Factor Analysis with Varimax Performs Statistical Inference” by Rohe & Zeng Konstantin Siroki和Korbinian Strimmer对Rohe & Zeng的“Vintage Factor Analysis with variimax演出Statistical Inference”讨论的贡献

IF 5.8 1区数学 Q1 STATISTICS & PROBABILITY

Journal of the Royal Statistical Society Series B-Statistical Methodology

Pub Date : 2023-05-23 DOI: 10.1093/jrsssb/qkad055

Konstantin Siroki, K. Strimmer

引用次数: 0

Florian Pargent, David Goretzko and Timo von Oertzen’s contribution to the Discussion of “Vintage Factor Analysis with Varimax Performs Statistical Inference” by Rohe & Zeng Florian Pargent, David Goretzko和Timo von Oertzen对Rohe & Zeng的“Vintage Factor Analysis with variimax执行统计推断”讨论的贡献

IF 5.8 1区数学 Q1 STATISTICS & PROBABILITY

Journal of the Royal Statistical Society Series B-Statistical Methodology

Pub Date : 2023-05-23 DOI: 10.1093/jrsssb/qkad054

F. Pargent, D. Goretzko, Timo von Oertzen

引用次数: 1

Correction to: Ordering factorial experiments 修正:排序阶乘实验

IF 5.8 1区数学 Q1 STATISTICS & PROBABILITY

Journal of the Royal Statistical Society Series B-Statistical Methodology

Pub Date : 2023-05-16 DOI: 10.1093/jrsssb/qkad053

引用次数: 0

A model where the least trimmed squares estimator is maximum likelihood 最小二乘估计量为最大似然的一种模型

IF 5.8 1区数学 Q1 STATISTICS & PROBABILITY

Journal of the Royal Statistical Society Series B-Statistical Methodology

Pub Date : 2023-05-15 DOI: 10.1093/jrsssb/qkad028

Vanessa Berenguer-Rico, S. Johansen, B. Nielsen

The least trimmed squares (LTS) estimator is a popular robust regression estimator. It finds a subsample of h ‘good’ observations among n observations and applies least squares on that subsample. We formulate a model in which this estimator is maximum likelihood. The model has ‘outliers’ of a new type, where the outlying observations are drawn from a distribution with values outside the realized range of h ‘good’, normal observations. The LTS estimator is found to be h1/2 consistent and asymptotically standard normal in the location-scale case. Consistent estimation of h is discussed. The model differs from the commonly used ϵ-contamination models and opens the door for statistical discussion on contamination schemes, new methodological developments on tests for contamination as well as inferences based on the estimated good data.

最小裁剪二乘(LTS)估计量是一种常用的稳健回归估计量。它在n个观测值中找到h个“好”观测值的子样本，并对该子样本应用最小二乘。我们制定了一个模型，其中这个估计量是最大似然。该模型具有一种新类型的“异常值”，其中的异常值来自分布，其值超出了h个“良好”的正常观测值的实现范围。在位置尺度的情况下，LTS估计量是h1/2一致和渐近标准正态的。讨论了h的一致估计。该模型不同于常用的ϵ-contamination模型，并为污染方案的统计讨论、污染测试的新方法发展以及基于估计的良好数据的推论打开了大门。

引用次数: 2

Non-parametric inference about mean functionals of non-ignorable non-response data without identifying the joint distribution. 在不确定联合分布的情况下，对不可忽略的非响应数据的平均函数进行非参数推断。

IF 3.1 1区数学 Q1 STATISTICS & PROBABILITY

Journal of the Royal Statistical Society Series B-Statistical Methodology

Pub Date : 2023-05-08 eCollection Date: 2023-07-01 DOI: 10.1093/jrsssb/qkad047

Wei Li, Wang Miao, Eric Tchetgen Tchetgen

We consider identification and inference about mean functionals of observed covariates and an outcome variable subject to non-ignorable missingness. By leveraging a shadow variable, we establish a necessary and sufficient condition for identification of the mean functional even if the full data distribution is not identified. We further characterize a necessary condition for $\sqrt{n}$ -estimability of the mean functional. This condition naturally strengthens the identifying condition, and it requires the existence of a function as a solution to a representer equation that connects the shadow variable to the mean functional. Solutions to the representer equation may not be unique, which presents substantial challenges for non-parametric estimation, and standard theories for non-parametric sieve estimators are not applicable here. We construct a consistent estimator of the solution set and then adapt the theory of extremum estimators to find from the estimated set a consistent estimator of an appropriately chosen solution. The estimator is asymptotically normal, locally efficient and attains the semi-parametric efficiency bound under certain regularity conditions. We illustrate the proposed approach via simulations and a real data application on home pricing.

我们考虑的是观测协变量和结果变量的均值函数的识别和推断，这些协变量和结果变量存在不可忽略的缺失。通过利用影子变量，我们建立了一个必要且充分的条件，即使没有识别出完整的数据分布，也能识别出均值函数。我们进一步描述了平均函数 n 次可估计性的必要条件。这个条件自然加强了识别条件，它要求存在一个函数，作为连接影子变量和均值函数的代表方程的解。代表方程的解可能不是唯一的，这给非参数估计带来了巨大挑战，非参数筛估计器的标准理论在此并不适用。我们构建了一个解集的一致估计器，然后利用极值估计器理论，从估计的解集中找到一个适当选择的解的一致估计器。该估计器具有渐近正态性、局部高效性，并在某些规则性条件下达到了半参数效率约束。我们通过模拟和房屋定价的真实数据应用来说明所提出的方法。

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引用次数: 0

Sparse Kronecker product decomposition: a general framework of signal region detection in image regression 稀疏Kronecker积分解:图像回归中信号区域检测的一般框架

1区数学 Q1 STATISTICS & PROBABILITY

Journal of the Royal Statistical Society Series B-Statistical Methodology

Pub Date : 2023-04-27 DOI: 10.1093/jrsssb/qkad024

Sanyou Wu, Long Feng

Abstract This paper aims to present the first Frequentist framework on signal region detection in high-resolution and high-order image regression problems. Image data and scalar-on-image regression are intensively studied in recent years. However, most existing studies on such topics focussed on outcome prediction, while the research on region detection is rather limited, even though the latter is often more important. In this paper, we develop a general framework named Sparse Kronecker Product Decomposition (SKPD) to tackle this issue. The SKPD framework is general in the sense that it works for both matrices and tensors represented image data. Our framework includes one-term, multi-term, and nonlinear SKPDs. We propose nonconvex optimization problems for one-term and multi-term SKPDs and develop path-following algorithms for the nonconvex optimization. Under a Restricted Isometric Property, the computed solutions of the path-following algorithm are guaranteed to converge to the truth with a particularly chosen initialization even though the optimization is nonconvex. Moreover, the region detection consistency could also be guaranteed. The nonlinear SKPD is highly connected to shallow convolutional neural networks (CNN), particularly to CNN with one convolutional layer and one fully-connected layer. Effectiveness of SKPD is validated by real brain imaging data in the UK Biobank database.

摘要本文旨在提出高分辨率和高阶图像回归问题中信号区域检测的第一个频域框架。近年来，图像数据和图像上的标量回归得到了广泛的研究。然而，现有的研究大多集中在结果预测上，而对区域检测的研究却相当有限，尽管后者往往更为重要。在本文中，我们开发了一个名为稀疏Kronecker积分解(SKPD)的通用框架来解决这个问题。SKPD框架是通用的，因为它既适用于表示图像数据的矩阵，也适用于表示图像数据的张量。我们的框架包括单项、多项和非线性skpd。我们提出了单项和多项skpd的非凸优化问题，并开发了非凸优化的路径跟踪算法。在有限等距性质下，路径跟踪算法的计算解在特定的初始化条件下收敛于真值，即使优化是非凸的。此外，还可以保证区域检测的一致性。非线性SKPD与浅卷积神经网络(CNN)具有高度的连接，特别是与具有一个卷积层和一个全连接层的CNN。SKPD的有效性通过英国生物银行数据库中的真实脑成像数据得到验证。

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引用次数: 0

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