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随机权重矩阵与解释变量下空间自回归模型的拟得分匹配估计AI 解读

With the rapid advancements in technology for data collection, the application of the spatial autoregressive (SAR) model has become increasingly prevalent in real-world analysis, particularly when dealing with large datasets. However, the commonly used quasi-maximum likelihood estimation (QMLE) for the SAR model is not computationally scalable to handle the data with a large size. In addition, when establishing the asymptotic properties of the parameter estimators of the SAR…

非欧随机对象的稳健函数主成分分析AI 解读

Summary Functional data analysis offers a diverse toolkit of statistical methods tailored to analysing samples of real-valued random functions. Recently, samples of time-varying random objects, such as time-varying networks, have been increasingly encountered in data analysis. These data structures represent elements within general metric spaces that lack local or global linear structures, rendering traditional functional data analysis methods inapplicable. Moreover, the…

固定与随机协变量下的协方差回归分析AI 解读

Covariance regression analysis is an approach to linking the covariance of responses to a set of explanatory variables X, where X can be a vector, matrix, or tensor. Most of the literature on this topic focuses on the “Fixed-X” setting and treats X as nonrandom. By contrast, treating explanatory variables X as random, namely the “Random-X” setting, is often more realistic in practice. This article aims to fill this gap in the literature on the estimation and model assessment…

含高维协变量的惩罚稀疏协方差回归AI 解读

Covariance regression offers an effective way to model the large covariance matrix with the auxiliary similarity matrices. In this work, we propose a sparse covariance regression (SCR) approach to handle the potentially high-dimensional predictors (i.e., similarity matrices). Specifically, we use the penalization method to identify the informative predictors and estimate their associated coefficients simultaneously. We first investigate the Lasso estimator and subsequently…

一般线性结构与增长参数维度的协方差模型AI 解读

For estimating the large covariance matrix with a limited sample size, we propose the covariance model with general linear structure (CMGL) by employing the general link function to connect the covariance of the continuous response vector to a linear combination of weight matrices. Without assuming the distribution of responses, and allowing the number of parameters associated with weight matrices to diverge, we obtain the quasi-maximum likelihood estimators (QMLE) of…

网络节点的向内与向外影响分析AI 解读

Measuring heterogeneous influence across nodes in a network is critical in network analysis. This article proposes an inward and outward network influence (IONI) model to assess nodal heterogeneity. Specifically, we allow for two types of influence parameters; one measures the magnitude of influence that each node exerts on others (outward influence), while we introduce a new parameter to quantify the receptivity of each node to being influenced by others (inward influence).…

协方差—均值回归的统计推断AI 解读

In this article, we introduce a covariance-mean regression model with heterogeneous similarity matrices. It not only links the covariance of responses to heterogeneous similarity matrices induced by auxiliary information, but also establishes the relationship between the mean of responses and covariates. Under this new model setting, however, two statistical inference challenges are encountered. The first challenge is that the consistency of the covariance estimator based on…

利用半监督学习插补高缺失率协变量AI 解读

Advancements in data collection techniques and the heterogeneity of data resources can yield high percentages of missing observations on variables, such as block-wise missing data. Under missing-data scenarios, traditional methods such as the simple average, k-nearest neighbor, multiple, and regression imputations may lead to results that are unstable or unable be computed. Motivated by the concept of semi-supervised learning, we propose a novel approach with which to fill…

大型精度矩阵元素的置信区域AI 解读

We consider the statistical inference for high-dimensional precision matrices. Specifically, we propose a data-driven procedure for constructing a class of simultaneous confidence regions for a subset of the entries of a large precision matrix. The confidence regions can be applied to test for specific structures of a precision matrix, and to recover its nonzero components. We first construct an estimator for the precision matrix via penalized node-wise regression. We then…

利用债券价格改进利率扩散模型的参数估计AI 解读

We consider improving estimating parameters of diffusion processes for interest rates by incorporating information in bond prices. This is designed to improve the estimation of the drift parameters, which are known to be subject to large estimation errors. It is shown that having the bond prices together with the short rates leads to more efficient estimation of all parameters for the interest rate models. It enhances the estimation efficiency of the maximum likelihood…

协方差回归分析AI 解读

This article introduces covariance regression analysis for a p-dimensional response vector. The proposed method explores the regression relationship between the p-dimensional covariance matrix and auxiliary information. We study three types of estimators: maximum likelihood, ordinary least squares, and feasible generalized least squares estimators. Then, we demonstrate that these regression estimators are consistent and asymptotically normal. Furthermore, we obtain the high…