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

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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

Manifold lifting: scaling Markov chain Monte Carlo to the vanishing noise regime 流形提升:缩放马尔可夫链蒙特卡洛到消失的噪声状态

IF 5.8 1区数学 Q1 STATISTICS & PROBABILITY

Journal of the Royal Statistical Society Series B-Statistical Methodology

Pub Date : 2023-04-24 DOI: 10.1093/jrsssb/qkad023

K. Au, Matthew M. Graham, Alexandre Hoang Thiery

Standard Markov chain Monte Carlo methods struggle to explore distributions that concentrate in the neighbourhood of low-dimensional submanifolds. This pathology naturally occurs in Bayesian inference settings when there is a high signal-to-noise ratio in the observational data but the model is inherently over-parametrised or nonidentifiable. In this paper, we propose a strategy that transforms the original sampling problem into the task of exploring a distribution supported on a manifold embedded in a higher-dimensional space; in contrast to the original posterior this lifted distribution remains diffuse in the limit of vanishing observation noise. We employ a constrained Hamiltonian Monte Carlo method, which exploits the geometry of this lifted distribution, to perform efficient approximate inference. We demonstrate in numerical experiments that, contrarily to competing approaches, the sampling efficiency of our proposed methodology does not degenerate as the target distribution to be explored concentrates near low-dimensional submanifolds. Python code reproducing the results is available at https://doi.org/10.5281/zenodo.6551654.

标准马尔可夫链蒙特卡罗方法难以探索集中在低维子流形附近的分布。当观测数据的信噪比很高，但模型本身过度参数化或不可识别时，这种病理自然发生在贝叶斯推理设置中。在本文中，我们提出了一种策略，将原始采样问题转化为探索嵌入在高维空间中的流形上支持的分布的任务;与原始后验相反，这种提升的分布在观测噪声消失的极限内保持弥漫性。我们采用约束哈密顿蒙特卡罗方法，利用这种提升分布的几何形状，来执行有效的近似推理。我们在数值实验中证明，与竞争方法相反，我们提出的方法的采样效率不会退化，因为要探索的目标分布集中在低维子流形附近。可从https://doi.org/10.5281/zenodo.6551654获得重现结果的Python代码。

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引用次数: 1

Ordering factorial experiments 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 : 2023-04-20 DOI: 10.1093/jrsssb/qkad027

Liuqing Yang, Yongdao Zhou, Min-Qian Liu

In many practical experiments, both the level combinations of factors and the addition orders will affect the responses. However, virtually no construction methods have been provided for such experimental designs. This paper focuses on such experiments, introduces a new type of design called the ordering factorial design, and proposes the nominal main effect component-position model and interaction-main effect component-position model. To obtain efficient fractional designs, we provide some deterministic construction methods. The resulting designs are D-optimal, and the run sizes are much smaller than that of the full designs. Moreover, in some cases, some constructed designs are still D-optimal after reducing the number of components and factors.

在许多实际实验中，因子的水平组合和加成顺序都会影响响应。然而，实际上没有为这种实验设计提供施工方法。本文针对这类实验，提出了一种新型的排序因子设计，并提出了名义主效应成分-位置模型和交互主效应成分-位置模型。为了获得有效的分式设计，我们提供了一些确定性的构造方法。所得到的设计是d最优的，并且运行尺寸比完整设计的运行尺寸小得多。此外，在某些情况下，一些构建的设计在减少组件和因素的数量后仍然是d最优的。

引用次数: 0

Peter J Bickel, Derek Bean, Aiyou Chen and Purnamrita Sarkar’s contribution to the Discussion of “Vintage Factor Analysis with Varimax Performs Statistical Inference” by Rohe & Zeng Peter J Bickel, Derek Bean, Aiyou Chen和Purnamrita Sarkar对Rohe & Zeng的“Vintage Factor Analysis with Varimax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 : 2023-04-12 DOI: 10.1093/jrsssb/qkad037

引用次数: 0

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