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Exact Simulation of Max-Infinitely Divisible Processes 最大不可分割过程的精确模拟

IF 1.9 Q2 ECONOMICS

Econometrics and Statistics

Pub Date : 2024-04-01 DOI: 10.1016/j.ecosta.2022.02.007

Peng Zhong , Raphaël Huser , Thomas Opitz

Max-infinitely divisible (max-id) processes play a central role in extreme-value theory and include the subclass of all max-stable processes. They allow for a constructive representation based on the pointwise maximum of random functions drawn from a Poisson point process defined on a suitable function space. Simulating from a max-id process is often difficult due to its complex stochastic structure, while calculating its joint density in high dimensions is often numerically infeasible. Therefore, exact and efficient simulation techniques for max-id processes are useful tools for studying the characteristics of the process and for drawing statistical inferences. Inspired by the simulation algorithms for max-stable processes, theory and algorithms to generalize simulation approaches tailored for certain flexible (existing or new) classes of max-id processes are presented. Efficient simulation for a large class of models can be achieved by implementing an adaptive rejection sampling scheme to sidestep a numerical integration step in the algorithm. The results of a simulation study highlight that our simulation algorithm works as expected and is highly accurate and efficient, such that it clearly outperforms customary approximate sampling schemes. As a by-product, new max-id models, which can be represented as pointwise maxima of general location-scale mixtures and possess flexible tail dependence structures capturing a wide range of asymptotic dependence scenarios, are also developed.

最大无限可分（max-id）过程在极值理论中起着核心作用，包括所有最大稳定过程的子类。它们允许基于从定义在合适函数空间上的泊松点过程中抽取的随机函数的点最大值进行构造表示。由于 max-id 过程具有复杂的随机结构，因此通常很难对其进行模拟，而在高维度上计算其联合密度通常在数值上也不可行。因此，精确而高效的 max-id 过程仿真技术是研究过程特征和得出统计推论的有用工具。受最大稳定过程仿真算法的启发，本文提出了针对某些灵活的（现有的或新的）最大 ID 过程类别的通用仿真方法的理论和算法。通过实施自适应剔除采样方案，避开算法中的数值积分步骤，可以实现对一大类模型的高效模拟。仿真研究的结果表明，我们的仿真算法正如预期的那样有效、精确和高效，因此明显优于传统的近似采样方案。作为副产品，我们还开发了新的 max-id 模型，该模型可表示为一般位置尺度混合物的点状最大值，并具有灵活的尾部依赖结构，可捕捉各种渐近依赖情况。

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引用次数: 0

A model specification test for semiparametric nonignorable missing data modeling 半参数非可变缺失数据建模的模型规范检验

IF 1.9 Q2 ECONOMICS

Econometrics and Statistics

Pub Date : 2024-04-01 DOI: 10.1016/j.ecosta.2021.08.005

Cheng Yong Tang

The instrumental variable approaches have been demonstrated effective for semiparametrically modeling the propensity function in analyzing data that may be missing not at random. A model specification test is considered for a class of parsimonious semiparametric propensity models. The test is constructed based on assessing an over-identification so as to detect possible incompatibility in the moment conditions when the model and/or instrumental variables are misspecified. Validity of the test under the null hypothesis is established; and its power is studied when the model is misspecified. A data analysis and simulations are presented to demonstrate the effectiveness of our methods.

在分析可能非随机缺失的数据时，工具变量方法已被证明能有效地对倾向函数进行半参数建模。本文考虑对一类半参数倾向模型进行模型规格检验。该检验以评估过度识别为基础，以便在模型和/或工具变量被错误定义时，检测时刻条件中可能存在的不相容性。该检验在零假设下的有效性得以确定；当模型被错误地指定时，对其有效性进行了研究。本文通过数据分析和模拟来证明我们方法的有效性。

引用次数: 0

Tandem clustering with invariant coordinate selection 带有不变坐标选择的串联聚类

IF 1.9 Q2 ECONOMICS

Econometrics and Statistics

Pub Date : 2024-03-16 DOI: 10.1016/j.ecosta.2024.03.002

Andreas Alfons, Aurore Archimbaud, Klaus Nordhausen, Anne Ruiz-Gazen

For multivariate data, tandem clustering is a well-known technique aiming to improve cluster identification through initial dimension reduction. Nevertheless, the usual approach using principal component analysis (PCA) has been criticized for focusing solely on inertia so that the first components do not necessarily retain the structure of interest for clustering. To address this limitation, a new tandem clustering approach based on invariant coordinate selection (ICS) is proposed. By jointly diagonalizing two scatter matrices, ICS is designed to find structure in the data while providing affine invariant components. Certain theoretical results have been previously derived and guarantee that under some elliptical mixture models, the group structure can be highlighted on a subset of the first and/or last components. However, ICS has garnered minimal attention within the context of clustering. Two challenges associated with ICS include choosing the pair of scatter matrices and selecting the components to retain. For effective clustering purposes, it is demonstrated that the best scatter pairs consist of one scatter matrix capturing the within-cluster structure and another capturing the global structure. For the former, local shape or pairwise scatters are of great interest, as is the minimum covariance determinant (MCD) estimator based on a carefully chosen subset size that is smaller than usual. The performance of ICS as a dimension reduction method is evaluated in terms of preserving the cluster structure in the data. In an extensive simulation study and empirical applications with benchmark data sets, various combinations of scatter matrices as well as component selection criteria are compared in situations with and without outliers. Overall, the new approach of tandem clustering with ICS shows promising results and clearly outperforms the PCA-based approach.

对于多变量数据，串联聚类是一种众所周知的技术，旨在通过初始维度的降低来改进聚类识别。然而，使用主成分分析（PCA）的通常方法受到了批评，因为它只关注惯性，所以第一成分并不一定能保留聚类所需的结构。为了解决这一局限性，我们提出了一种基于不变坐标选择（ICS）的新串联聚类方法。通过对两个散点矩阵进行联合对角，ICS 可以找到数据中的结构，同时提供仿射不变成分。之前已经得出了一些理论结果，并保证在某些椭圆混合物模型下，可以在第一个和/或最后一个分量的子集上突出组结构。然而，ICS 在聚类中获得的关注极少。与 ICS 相关的两个挑战包括选择一对散点矩阵和选择要保留的成分。事实证明，为了达到有效聚类的目的，最佳散点对由一个捕捉簇内结构的散点矩阵和另一个捕捉全局结构的散点矩阵组成。对于前者来说，局部形状或成对散点是非常重要的，基于比通常更小的精心选择的子集大小的最小协方差行列式（MCD）估计器也是如此。ICS 作为一种降维方法，其性能是通过保留数据中的聚类结构来评估的。在广泛的模拟研究和基准数据集的经验应用中，比较了有异常值和无异常值情况下的各种散点矩阵组合以及成分选择标准。总之，采用 ICS 的串联聚类新方法显示出良好的效果，明显优于基于 PCA 的方法。

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引用次数: 0

Stein-Like Shrinkage Estimators for Coefficients of a Single-Equation in Simultaneous Equation Systems 同时方程系统中单项式系数的斯坦式收缩估计器

IF 1.9 Q2 ECONOMICS

Econometrics and Statistics

Pub Date : 2024-03-08 DOI: 10.1016/j.ecosta.2024.03.001

A, l, i, , M, e, h, r, a, b, a, n, i

Two stein-like shrinkage estimators are introduced to modify the 2SLS and the LIML estimators for coefficients of a single equation in a simultaneous system of equations. The proposed estimators are weighted averages of the 2SLS/LIML estimators and the OLS estimator. The shrinkage weight depends on the Wu-Hausman misspecification test statistic which evaluates the null of exogeneity against the alternative hypothesis of endogeneity. The approximate finite sample bias, mean squared errors, and density functions of the Stein-like shrinkage estimators are obtained using small-disturbance approximations. The dominance conditions of the Stein-like shrinkage estimators over the 2SLS/LIML estimator under the mean squared error and the concentration probability are obtained. The proposed method is further illustrated by simulation studies which demonstrate the good finite sample performance of the method, and is also applied to an empirical application of returns to education.

本文引入了两个类似于斯坦因收缩的估计器，用于修正同时方程组中单个方程系数的 2SLS 和 LIML 估计器。所提出的估计器是 2SLS/LIML 估计器和 OLS 估计器的加权平均值。缩减权重取决于吴-豪斯曼（Wu-Hausman）失范检验统计量，该统计量针对内生性的替代假设评估外生性的零假设。利用小扰动近似法获得了斯坦因类收缩估计器的近似有限样本偏差、均方误差和密度函数。在均方误差和集中概率下，得到了斯坦因类收缩估计器相对于 2SLS/LIML 估计器的优势条件。模拟研究进一步说明了所提出的方法，证明该方法具有良好的有限样本性能，并将其应用于教育回报的实证应用中。

引用次数: 0

Comments on “Challenges of cellwise outliers” by Jakob Raymaekers and Peter J. Rousseeuw 对 Jakob Raymaekers 和 Peter J. Rousseeuw 所作 "细胞离群值的挑战 "的评论

IF 1.9 Q2 ECONOMICS

Econometrics and Statistics

Pub Date : 2024-02-24 DOI: 10.1016/j.ecosta.2024.02.003

Claudio Agostinelli

引用次数: 0

Challenges of cellwise outliers 单元离群值的挑战

IF 1.9 Q2 ECONOMICS

Econometrics and Statistics

Pub Date : 2024-02-17 DOI: 10.1016/j.ecosta.2024.02.002

Jakob Raymaekers, Peter J. Rousseeuw

It is well-known that real data often contain outliers. The term outlier typically refers to a case, typically denoted by a row of the data matrix. In recent times a different type has come into focus, the cellwise outliers. These are suspicious cells (entries) that can occur anywhere in the data matrix. Even a relatively small proportion of outlying cells can contaminate over half the cases, which is a problem for robust methods. This article discusses the challenges posed by cellwise outliers, and some methods developed so far to deal with them. New results are obtained on cellwise breakdown values for location, covariance and regression. A cellwise robust method is proposed for correspondence analysis, with real data illustrations. The paper concludes by formulating some points for debate.

众所周知，真实数据中常常包含离群值。离群值通常是指数据矩阵中的某一行。近来，一种不同类型的离群值--单元离群值开始受到关注。这些可疑的单元格（条目）可能出现在数据矩阵的任何位置。即使是比例相对较小的离群单元，也会污染一半以上的案例，这对稳健方法来说是个问题。本文讨论了单元异常值带来的挑战，以及迄今为止开发的一些处理方法。本文获得了关于位置、协方差和回归的单元击穿值的新结果。本文提出了一种用于对应分析的单元稳健方法，并提供了实际数据说明。论文最后提出了一些讨论要点。

引用次数: 0

Bayesian Nonparametric Multivariate Mixture of Autoregressive Processes with Application to Brain Signals 贝叶斯非参数多变量自回归过程混合物在脑信号中的应用

IF 1.9 Q2 ECONOMICS

Econometrics and Statistics

Pub Date : 2024-02-17 DOI: 10.1016/j.ecosta.2024.01.004

Guillermo Granados-Garcia, Raquel Prado, Hernando Ombao

One of neuroscience’s goals is to study the interactions between different brain regions during rest and while performing specific cognitive tasks. Multivariate Bayesian autoregressive decomposition (MBMARD) is proposed as an intuitive and novel Bayesian non-parametric model to represent high-dimensional signals as a low-dimensional mixture of univariate uncorrelated latent oscillations. Each latent oscillation captures a specific underlying oscillatory activity and, hence, is modeled as a unique second-order autoregressive process due to a compelling property, namely, that its spectral density’s shape is characterized by a unique frequency peak and bandwidth, parameterized by a location and a scale parameter. The posterior distributions of the latent oscillation parameters are computed using a Metropolis-within-Gibbs algorithm. One of the advantages of the MBMARD model is its higher robustness against misspecification, compared with standard models. The main scientific questions addressed by the MBMARD model relate to the effects of long-term alcohol abuse on memory. These effects were examined by analyzing the electroencephalogram records of alcoholic and non-alcoholic subjects performing a visual recognition experiment. The MBMARD model yielded novel and interesting findings, including the identification of subject-specific clusters of low- and high-frequency oscillations in different brain regions.

神经科学的目标之一是研究不同脑区在休息和执行特定认知任务时的相互作用。多变量贝叶斯自回归分解（MBMARD）是一种直观、新颖的贝叶斯非参数模型，用于将高维信号表示为单变量不相关潜振荡的低维混合物。每个潜在振荡都捕捉到了特定的潜在振荡活动，因此，由于一个引人注目的特性，即其频谱密度的形状以独特的频率峰值和带宽为特征，并以位置和尺度参数为参数，因此被建模为一个独特的二阶自回归过程。使用 Metropolis-Within-Gibbs 算法计算潜在振荡参数的后验分布。与标准模型相比，MBMARD 模型的优势之一是对错误规范具有更高的鲁棒性。MBMARD 模型解决的主要科学问题涉及长期酗酒对记忆的影响。我们通过分析酗酒者和非酗酒者在进行视觉识别实验时的脑电图记录来研究这些影响。MBMARD 模型得出了新颖而有趣的发现，包括在不同脑区识别出特定受试者的低频和高频振荡群。

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引用次数: 0

Rejoinder to the comment of Agostinelli 对阿戈斯蒂内利评论的反驳

IF 1.9 Q2 ECONOMICS

Econometrics and Statistics

Pub Date : 2024-02-17 DOI: 10.1016/j.ecosta.2024.02.004

Jakob Raymaekers, Peter J. Rousseeuw

引用次数: 0

Shared Differential Clustering across Single-cell RNA Sequencing Datasets with the Hierarchical Dirichlet Process 利用分层 Dirichlet 过程对单细胞 RNA 测序数据集进行共享差异聚类

IF 1.9 Q2 ECONOMICS

Econometrics and Statistics

Pub Date : 2024-02-17 DOI: 10.1016/j.ecosta.2024.02.001

Jinlu Liu, Sara Wade, Natalia Bochkina

Single-cell RNA sequencing (scRNA-seq) is a powerful technology that allows researchers to understand gene expression patterns at the single-cell level and uncover the heterogeneous nature of cells. Clustering is an important tool in scRNA-seq analysis to discover groups of cells with similar gene expression patterns and identify potential cell types. Integration of multiple scRNA-seq datasets is a pressing challenge, and in this direction, a novel model is developed to extend clustering methods to appropriately combine inference across multiple datasets. The model simultaneously addresses normalization to deal with the inherent noise and uncertainty in scRNA-seq, infers cell types, and integrates multiple datasets for shared clustering in principled manner through a hierarchical Bayesian framework. A Gibbs sampler is developed that copes with the high-dimensionality of scRNA-seq through consensus clustering. The methodological developments are driven by experimental data from embryonic cells, with the aim of understanding the role of PAX6 in prenatal development, and more specifically how cell-subtypes and their proportions change when knocking out this factor.

单细胞 RNA 测序（scRNA-seq）是一项功能强大的技术，可让研究人员了解单细胞水平的基因表达模式，并揭示细胞的异质性。聚类是 scRNA-seq 分析中的一个重要工具，可用于发现具有相似基因表达模式的细胞群，并识别潜在的细胞类型。整合多个 scRNA-seq 数据集是一个紧迫的挑战，为此，我们开发了一个新模型来扩展聚类方法，以适当地结合多个数据集的推论。该模型同时解决了归一化问题，以处理 scRNA-seq 中固有的噪声和不确定性，推断细胞类型，并通过分层贝叶斯框架，以原则性的方式整合多个数据集，实现共享聚类。开发的吉布斯采样器可通过共识聚类来应对 scRNA-seq 的高维性。方法论的发展是由胚胎细胞的实验数据驱动的，目的是了解 PAX6 在产前发育中的作用，更具体地说，当敲除该因子时，细胞亚型及其比例是如何变化的。

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引用次数: 0

Multivariate Hermite polynomials and information matrix tests 多元赫米特多项式和信息矩阵检验

IF 1.9 Q2 ECONOMICS

Econometrics and Statistics

Pub Date : 2024-02-06 DOI: 10.1016/j.ecosta.2024.01.005

Dante Amengual, Gabriele Fiorentini, Enrique Sentana

The information matrix test for a normal random vector is shown to coincide with the sum of the moment tests for all third- and fourth-order multivariate Hermite polynomials. The statistic is decomposed as the sum of the marginal information matrix test for a subvector, the conditional information matrix test for the complementary subvector, and a third leftover component. It is also shown that exact finite sample distributions can be obtained by drawing spherical Gaussian vectors and orthogonalising them using sample moments. These tests are applied to assess the implications of Gibrat’s law for US city sizes using the three most recent censuses.

正态随机向量的信息矩阵检验与所有三阶和四阶多变量赫米特多项式的矩检验之和相吻合。统计量被分解为一个子向量的边际信息矩阵检验、互补子向量的条件信息矩阵检验和第三个剩余部分之和。研究还表明，通过绘制球形高斯向量并使用样本矩对其进行正交，可以获得精确的有限样本分布。这些检验应用于利用最近三次人口普查评估吉布拉特定律对美国城市规模的影响。

引用次数: 0

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