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通过近似消息传递实现高维 Newey–Powell 检验AI 解读

We propose a high-dimensional extension of the heteroscedasticity test proposed in Newey and Powell (1987). Our test is based on expectile regression in the proportional asymptotic regime where $n/p \to \delta \in (0,1]$ . The asymptotic analysis of the test statistic uses the approximate message passing algorithm, from which we obtain the limiting distribution of the test and establish its asymptotic power. The numerical performance of the test is validated through an…

基于多样化投影的含潜在因子高维空间自回归AI 解读

We study one particular type of multivariate spatial autoregression (MSAR) model with diverging dimensions in both responses and covariates. This makes the usual MSAR models no longer applicable due to the high computational cost. To address this issue, we propose a factor-augmented spatial autoregression (FSAR) model. FSAR is a special case of MSAR but with a novel factor structure imposed on the high-dimensional random error vector. The latent factors of FSAR are assumed…

具有空间依赖与缺失数据的自回归模型AI 解读

We study herein an autoregressive model with spatially correlated error terms and missing data. A logistic regression model with completely observed covariates is used to model the missingness mechanism. An autoregressive model is used to accommodate time series dependence, and a spatial error model is used to capture spatial dependence. To estimate the model, a weighted least squares estimator is developed for the temporal component, and a weighted maximum likelihood…

线性回归系数与误差方差结构变化的联合检验AI 解读

We provide a comprehensive treatment for the problem of testing jointly for structural changes in both the regression coefficients and the variance of the errors in a single equation system involving stationary regressors. Our framework is quite general in that we allow for general mixing‐type regressors and the assumptions on the errors are quite mild. Their distribution can be nonnormal and conditional heteroskedasticity is permitted. Extensions to the case with serially…

基于抽样网络数据的空间自相关估计AI 解读

Spatial autocorrelation is a parameter of importance for network data analysis. To estimate spatial autocorrelation, maximum likelihood has been popularly used. However, its rigorous implementation requires the whole network to be observed. This is practically infeasible if network size is huge (e.g., Facebook, Twitter, Weibo, WeChat, etc.). In that case, one has to rely on sampled network data to infer about spatial autocorrelation. By doing so, network relationships (i.e.,…

大型稀疏张量的贝叶斯分解AI 解读

It has become routine to collect data that are structured as multiway arrays (tensors). There is an enormous literature on low rank and sparse matrix factorizations, but limited consideration of extensions to the tensor case in statistics. The most common low rank tensor factorization relies on parallel factor analysis (PARAFAC), which expresses a rank k tensor as a sum of rank one tensors. When observations are only available for a tiny subset of the cells of a big tensor,…

检测持久性多重结构变化的 Wald 检验AI 解读

This paper considers the problem of testing for multiple structural changes in the persistence of a univariate time series. We propose sup-Wald tests of the null hypothesis that the process has an autoregressive unit root throughout the sample against the alternative hypothesis that the process alternates between stationary and unit root regimes. We derive the limit distributions of the tests under the null and establish their consistency under the relevant alternatives. We…