Journal of Multivariate Analysis最新文献

英文中文

Estimation of tensor factor model by iterative least squares 张量因子模型的迭代最小二乘估计

IF 1.4 3区数学 Q2 STATISTICS & PROBABILITY

Journal of Multivariate Analysis

Pub Date : 2025-11-28 DOI: 10.1016/j.jmva.2025.105557

Yong He , Yujie Hou , Yalin Wang , Wen-Xin Zhou

For large-dimensional tensor time series, dimension reduction plays a pivotal role. Tensor factor model depicts tensor-valued time series through a low-dimensional projection on a space of common factors, thereby achieving great dimension reduction and having a wide range of applications in economics and finance. In this paper, we propose a simple iterative least squares algorithm for estimating tensor factor model. We first estimate the latent common factors by using deterministic mode-

k

projection matrices and then estimate the loading matrices by minimizing the squared Frobenius loss function under certain identifiability conditions. The estimated loading matrices are further taken as new mode-

k

projection matrices, and the above update procedures are iteratively executed until convergence. We also propose a novel eigenvalue ratio method for estimating the number of factors and show the consistency of the estimators. Given the true number of factors, we theoretically establish the convergence rates of the estimated loading matrices and signal components at the

s

th iteration for any

s \geq 1

. Thorough numerical studies are conducted to investigate the finite-sample performance of the proposed method. Analyses of import-export transport networks and lung cancer histopathological image datasets illustrate the empirical usefulness of the proposed method.

对于大维张量时间序列，降维起着至关重要的作用。张量因子模型通过在公共因子空间上的低维投影来描述张量值时间序列，从而实现了极大的降维，在经济和金融领域有着广泛的应用。本文提出了一种简单的迭代最小二乘算法来估计张量因子模型。首先利用确定性模式k投影矩阵估计潜在的公共因子，然后在一定的可辨识性条件下，通过最小化Frobenius损失函数的平方来估计加载矩阵。将估计的加载矩阵作为新的k型投影矩阵，迭代执行上述更新过程直至收敛。我们还提出了一种新的估计因子数量的特征值比方法，并证明了估计量的一致性。在给定因子的真实数目的情况下，我们从理论上建立了对任意s≥1的估计加载矩阵和信号分量在第5次迭代时的收敛速率。对该方法的有限样本性能进行了深入的数值研究。对进出口运输网络和肺癌组织病理学图像数据集的分析说明了所提出方法的经验有效性。

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引用次数: 0

Asymptotics for a discounted systemic risk measure in a multi-dimensional risk model with dependent claim sizes and stochastic return 具有独立索赔规模和随机收益的多维风险模型中贴现系统风险测度的渐近性

IF 1.4 3区数学 Q2 STATISTICS & PROBABILITY

Journal of Multivariate Analysis

Pub Date : 2025-11-28 DOI: 10.1016/j.jmva.2025.105569

Yang Yang , Zhenyuan Xu , Yahui Fan

Consider a multi-dimensional renewal risk model, in which an insurer simultaneously operates more than one line of business, and is allowed to make both risk-free and risky investments. The claim sizes from all business lines are triggered by a series of common shocks, whose arrival times constitute a renewal counting process. The price process of the investment portfolio is described as a geometric Lévy process. In this study, we consider two cases that the claim sizes from different business lines are asymptotically dependent or asymptotically independent. Under the framework of regular variation, we study the asymptotic behavior of a discounted systemic risk measure, which is proposed by Li (2022) to describe the instant expected shortfall of the insurer at the moment when one of its business lines suffers crisis. The obtained results indicate that the asymptotics for the discounted systemic risk measure depend on neither the price process of the investment nor the renewal shock-number process, and, in addition, the asymptotic independence also gives no contribution to the asymptotic formula.

考虑一个多维续保风险模型，在该模型中，保险公司同时经营多条业务线，并允许进行无风险和有风险的投资。来自所有业务线的索赔大小由一系列常见冲击触发，其到达时间构成续期计数过程。投资组合的价格过程被描述为一个几何lsamvy过程。在本研究中，我们考虑了两种情况，即来自不同业务线的索赔规模是渐近相关的或渐近独立的。在规则变化的框架下，我们研究了Li（2022）提出的贴现系统风险测度的渐近行为，该测度描述了当保险公司的一条业务线遭受危机时的即时预期缺口。所得结果表明，贴现系统风险测度的渐近性既不依赖于投资价格过程，也不依赖于更新冲击数过程，而且渐近独立性对渐近公式也没有贡献。

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引用次数: 0

A general framework to extend sufficient dimension reductions to the cases of the mixture multivariate elliptical distributions 给出了将足够降维扩展到混合多元椭圆分布的一般框架

IF 1.4 3区数学 Q2 STATISTICS & PROBABILITY

Journal of Multivariate Analysis

Pub Date : 2025-11-28 DOI: 10.1016/j.jmva.2025.105551

Wenjuan Li , Hongming Pei , Ali Jiang , Fei Chen

In the sufficient dimension reduction (SDR), many methods depend on some assumptions on the distribution of predictor vector, such as the linear design condition (L.D.C.), the assumption of constant conditional variance, and so on. The mixture distributions emerge frequently in practice, but they may not satisfy the above assumptions. In this article, a general framework is proposed to extend various SDR methods to the cases where the predictor vector follows the mixture elliptical distributions, together with the asymptotic property for the consistency of the kernel matrix estimators. For illustration, the extensions of several classical SDR approaches under the proposed framework are detailed. Moreover, a method to estimate the structural dimension is given, together with a procedure to check an assumption called homogeneity. The proposed methodology is illustrated by simulated and real examples.

在充分降维（SDR）中，许多方法依赖于对预测向量分布的一些假设，如线性设计条件（L.D.C.）、条件方差恒定假设等。混合分布在实践中经常出现，但它们可能不满足上述假设。本文提出了一个一般框架，将各种SDR方法扩展到预测向量服从混合椭圆分布的情况，并给出了核矩阵估计量相合性的渐近性质。为了说明这一点，详细介绍了几种经典SDR方法在该框架下的扩展。此外，还给出了一种估计结构尺寸的方法，以及一种检验均匀性假设的方法。通过仿真和实际算例说明了所提出的方法。

引用次数: 0

Varying-coefficient quantile regression with effect under panel data and missing observation 在面板数据和缺失观测下的变系数分位数回归

IF 1.4 3区数学 Q2 STATISTICS & PROBABILITY

Journal of Multivariate Analysis

Pub Date : 2025-11-28 DOI: 10.1016/j.jmva.2025.105561

Shu-Yu Li , Han-Ying Liang , Bao-Hua Wang

We, in this paper, focus on partial linear varying-coefficient quantile regression with fixed effects under panel data and missing observations, where the missing observations include either responses or covariates are missing at random. Under independent setting, we define estimators of the unknown parameter vector, varying-coefficient function and effect in the model, and discuss their large number properties. To use the information from within-subject correlations, we propose weighted estimators for the unknown amounts, where the weights are chosen based on mean and quantile regressions, respectively, by quadratic inference technique and empirical likelihood method. Under dependent assumption, we establish asymptotic normality of the weighted estimators. Meanwhile, we study hypothesis tests of the parameter, varying-coefficient function and effect, and prove asymptotic distributions of restricted estimators and test statistics of the parameter under null hypothesis and local alternative hypothesis, respectively. Also, oracle property of the parameter is considered. Simulation study and real data analysis are conducted to evaluate the performance of the proposed methods.

本文主要研究面板数据和缺失观测值下固定效应的偏线性变系数分位数回归，其中缺失观测值包括随机缺失的响应或随机缺失的协变量。在独立设定下，定义了模型中未知参数向量、变系数函数和效应的估计量，并讨论了它们的大数性质。为了利用主体内相关性的信息，我们提出了未知数量的加权估计，其中权重分别基于均值和分位数回归，通过二次推理技术和经验似然方法选择。在相关假设下，我们建立了加权估计量的渐近正态性。同时，研究了参数、变系数函数和效应的假设检验，分别证明了零假设和局部备择假设下的约束估计量的渐近分布和参数的统计量检验。同时，还考虑了参数的oracle属性。通过仿真研究和实际数据分析，对所提方法的性能进行了评价。

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引用次数: 0

Jump detection in single-index models with measurement error 具有测量误差的单指标模型的跳跃检测

IF 1.4 3区数学 Q2 STATISTICS & PROBABILITY

Journal of Multivariate Analysis

Pub Date : 2025-11-28 DOI: 10.1016/j.jmva.2025.105574

Yuan Liu , Yan-Yong Zhao , Noriszura Ismail , Razik Ridzuan Mohd Tajuddin , Yuchun Zhang

Measurement error regression is widely used in statistical modeling. When the regression function is discontinuous, the estimation and inference have become challenging. In this paper, we develop a jump detection framework for a single index model with measurement error. First, for the single index model with measurement error, the consistent estimator of the index coefficient is obtained by using both the SIMEX (simulation extrapolation) and estimation equation methods. Then, the one-sided kernel local linear method is used to construct the estimator of the nonparametric function and the estimator of the jump point. Under some regularity assumptions, the asymptotic properties of the resultant estimators are established. The finite sample performance of our methodologies is evaluated by numerical simulation, and finally they are used to analyze the effect of serum cholesterol level and age on male blood.

测量误差回归在统计建模中得到了广泛的应用。当回归函数不连续时，估计和推理就变得很有挑战性。在本文中，我们开发了一个具有测量误差的单指标模型的跳跃检测框架。首先，针对具有测量误差的单指标模型，采用模拟外推法和估计方程法得到指标系数的一致估计量；然后，利用单侧核局部线性方法构造了非参数函数的估计量和跳点的估计量。在一些正则性假设下，给出了合成估计量的渐近性质。通过数值模拟对方法的有限样本性能进行了评价，最后应用该方法分析了血清胆固醇水平和年龄对男性血液的影响。

引用次数: 0

Testing multivariate normality for two-level structural equation models 两级结构方程模型的多元正态性检验

IF 1.4 3区数学 Q2 STATISTICS & PROBABILITY

Journal of Multivariate Analysis

Pub Date : 2025-11-28 DOI: 10.1016/j.jmva.2025.105562

Jiajuan Liang , Peter M. Bentler , Yiwen Cao

Multivariate normality is a common assumption in the maximum likelihood analysis of two-level structural equation models. Under the normal assumption, the independence condition on level-1 observations is no longer satisfied. As a result, existing statistics for testing multivariate normality based independent observations cannot be directly used for the same purpose in two-level structural equation models. In this paper we tackle this problem by employing the theory of spherical matrix distributions and some properties of invariant statistics. A series of necessary tests are constructed from some existing invariant statistics with a balanced level-1 sample design. These necessary tests are applicable without requiring a large level-1 or level-2 sample size. A Monte Carlo study is carried out to demonstrate the performance of the proposed tests in the aspects of controlling type I error rates, the power against a departure from multivariate normality for level-1 variables, and the power against a departure from multivariate normality for level-2 variables. An application of the necessary tests to a practical data set is illustrated.

多元正态性是两级结构方程模型最大似然分析中常见的假设。在正态假设下，一级观测值的独立性不再满足。因此，现有的用于检验基于独立观测的多元正态性的统计量不能直接用于两层结构方程模型的相同目的。本文利用球矩阵分布理论和不变统计的一些性质来解决这一问题。在平衡的一级样本设计下，从现有的一些不变统计量构造了一系列必要的检验。这些必要的测试适用于不需要大的一级或二级样本量。通过蒙特卡罗研究证明了所提出的测试在控制I型错误率、1级变量的抗偏离多元正态性的能力以及2级变量的抗偏离多元正态性的能力方面的性能。并举例说明了必要的测试在实际数据集上的应用。

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引用次数: 0

Fréchet kNN-based sufficient dimension reduction 基于knn的fresamet充分降维

IF 1.4 3区数学 Q2 STATISTICS & PROBABILITY

Journal of Multivariate Analysis

Pub Date : 2025-11-28 DOI: 10.1016/j.jmva.2025.105566

Xueyan Huang, Rui Qiu, Zhou Yu

In this paper, we introduce two Fréchet inverse regression methods with kernel bandwidths determined by

k

nearest neighbors, designed to achieve sufficient dimension reduction for a metric space-valued response and Euclidean predictors. A key advantage of the proposals lies in their ability to effectively preserve the intrinsic information of the metric space-valued response. We establish the asymptotic normality of these methods through rigorous theoretical proofs. Additionally, simulations and a real data example are provided to validate the performance and practical applicability of the proposed methods.

在本文中，我们介绍了两种核带宽由k近邻决定的fracimet逆回归方法，旨在为度量空间值响应和欧几里得预测实现足够的降维。这些建议的一个关键优势在于它们能够有效地保留度量空间值响应的内在信息。通过严格的理论证明，建立了这些方法的渐近正态性。最后，通过仿真和一个实际数据算例验证了所提方法的性能和实用性。

引用次数: 0

Type I multivariate Pólya-Aeppli distributions with applications 带应用程序的I型多变量Pólya-Aeppli发行版

IF 1.4 3区数学 Q2 STATISTICS & PROBABILITY

Journal of Multivariate Analysis

Pub Date : 2025-11-28 DOI: 10.1016/j.jmva.2025.105556

Claire Geldenhuys, Rene Ehlers, Andriette Bekker

An extensive body of literature exists that specifically addresses the univariate case of zero-inflated count models. In contrast, research pertaining to multivariate models is notably less developed. We propose two new parsimonious multivariate models that can be used to model correlated multivariate overdispersed count data. Furthermore, for different parameter settings and sample sizes, various simulations are performed. In conclusion, we demonstrate the performance of the newly proposed multivariate candidates on two benchmark datasets, which surpasses that of several alternative approaches.

有大量的文献专门论述了零膨胀计数模型的单变量情况。相比之下，与多变量模型有关的研究明显欠发达。我们提出了两个新的简化的多元模型，可以用来模拟相关的多元过分散计数数据。此外，对于不同的参数设置和样本量，进行了各种模拟。总之，我们证明了新提出的多变量候选算法在两个基准数据集上的性能优于几种替代方法。

引用次数: 0

On the two-sample Behrens–Fisher problem for high-dimensional data 高维数据的双样本Behrens-Fisher问题

IF 1.4 3区数学 Q2 STATISTICS & PROBABILITY

Journal of Multivariate Analysis

Pub Date : 2025-11-28 DOI: 10.1016/j.jmva.2025.105572

Yongshuai Chen , Gongming Shi , Xiaomeng Yan, Baoxue Zhang

In this paper, we study the limiting distribution of Chen-Qin’s test statistic and propose a novel weighted bootstrap test procedure for the high-dimensional two-sample Behrens–Fisher problem. We first show that the test statistic has an asymptotic null that is a mixture of a chi-square-type mixture distribution and a normal distribution, without imposing either the normal assumption or a factor-like model assumption on the underlying distributions. To gain insight into the asymptotic null distribution of the test statistic, we show that under stronger restrictions on the covariance matrices and the null hypothesis, the test statistic is either asymptotically normal or a chi-square-type mixture distribution. The power properties of the test are evaluated asymptotically under the high-dimensional local and fixed alternative hypothesis. We also derive that the proposed weighted bootstrap test procedure has correct test level asymptotically. Two simulation studies and a real data example show that the new weighted bootstrap procedure significantly outperforms other benchmarks in terms of size control and is comparable in terms of power.

本文研究了Chen-Qin检验统计量的极限分布，提出了一种新的高维双样本Behrens-Fisher问题的加权自举检验方法。我们首先证明检验统计量有一个渐近零值，它是卡方型混合分布和正态分布的混合物，而没有对底层分布施加正态假设或类因子模型假设。为了深入了解检验统计量的渐近零分布，我们表明，在对协方差矩阵和零假设的更强限制下，检验统计量要么是渐近正态分布，要么是卡方型混合分布。在高维局部定备假设下，渐近地评价了检验的幂性质。并渐近地证明了所提出的加权自举检验方法具有正确的检验水平。两个仿真研究和一个实际数据示例表明，新的加权自举过程在大小控制方面明显优于其他基准程序，并且在功率方面具有可比性。

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引用次数: 0

Variable selection in mixture regression for longitudinal data based on joint mean–covariance model 基于联合均值-协方差模型的纵向数据混合回归变量选择

IF 1.4 3区数学 Q2 STATISTICS & PROBABILITY

Journal of Multivariate Analysis

Pub Date : 2025-11-19 DOI: 10.1016/j.jmva.2025.105548

Jing Yu , Jianxin Pan

A large number of explanatory variables may be measured with the collection of longitudinal data, of which some may not be influential for modeling of heterogeneous longitudinal data. For such complex data, not only their mean but also covariances may be affected by various explanatory variables. A data-driven approach is proposed to model the mean and covariance structures, simultaneously, together with selecting influential explanatory variables. A penalized maximum likelihood method for the joint mean and covariance model is developed within the framework of finite Gaussian mixture regression. EM algorithm is employed for the numerical calculation. The parameter estimators obtained are shown to be consistent and asymptotically normally distributed, and have oracle properties with proper choices of penalty function and tuning parameter. Simulation studies show that the proposed method works very well and provides accurate and effective parameter estimators by conducting variable selection. For illustration, real data analysis on clustering COVID-19 infected cases for European countries in terms of governmental policy effects is made to demonstrate the usefulness of the proposed method.

通过收集纵向数据可以测量大量的解释变量，其中一些变量可能对异构纵向数据的建模没有影响。对于这种复杂的数据，不仅其均值，而且协方差都可能受到各种解释变量的影响。提出了一种数据驱动的方法，同时对均值和协方差结构进行建模，并选择有影响的解释变量。在有限高斯混合回归的框架内，对联合均值和协方差模型提出了一种惩罚极大似然法。采用EM算法进行数值计算。得到的参数估计量是一致的、渐近正态分布的，并且在适当选择惩罚函数和调优参数的情况下具有oracle性质。仿真研究表明，该方法通过变量选择提供了准确有效的参数估计。为了说明，从政府政策效应的角度对欧洲国家的聚集性COVID-19感染病例进行了实际数据分析，以证明所提出方法的有效性。

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