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面向大规模时空协变量的空间效应检测回归AI 解读

Abstract We develop a Spatial Effect Detection Regression (SEDR) model to capture the nonlinear and irregular effects of high-dimensional spatio-temporal predictors on a scalar outcome. Specifically, we assume that both the component and the coefficient functions in the SEDR are unknown smooth functions of location and time. This allows us to leverage spatially and temporally correlated information, transforming the curse of dimensionality into a blessing, as confirmed by…

高斯图模型的极小极大检测边界与精确最优检验AI 解读

Abstract In this article, we derive the minimax detection boundary for testing a sub-block of variables in a precision matrix under the Gaussian distribution. Compared to the results on the minimum rate of signals for testing precision matrices in literature, our result gives the exact minimum signal strength in a precision matrix that can be detected. We propose a thresholding test that is able to achieve the minimax detection boundary under certain cases by adaptively…

多层阈值法下的两样本高维协方差检验与信号识别AI 解读

The paper considers testing and signal identification for covariance matrices from two populations of marginally sub-Gaussian distributed. A multi-level thresholding procedure is proposed for testing the equality of two high-dimensional covariance matrices, which is designed to detect sparse and faint differences between the covariances. A novel U-statistic composition is developed to establish the asymptotic distribution of the thresholding statistics in conjunction with…

二阶平稳向量时间序列的主成分分析AI 解读

We extend the principal component analysis (PCA) to second-order stationary vector time series in the sense that we seek for a contemporaneous linear transformation for a $p$-variate time series such that the transformed series is segmented into several lower-dimensional subseries, and those subseries are uncorrelated with each other both contemporaneously and serially. Therefore, those lower-dimensional series can be analyzed separately as far as the linear dynamic…

高维广义线性模型的检验AI 解读

Summary We consider testing regression coefficients in high dimensional generalized linear models. By modifying the test statistic of Goeman and his colleagues for large but fixed dimensional settings, we propose a new test, based on an asymptotic analysis, that is applicable for diverging dimensions and is robust to accommodate a wide range of link functions. The power properties of the tests are evaluated asymptotically under two families of alternative hypotheses. In…

含潜在因子、内生性与非线性的高维随机回归AI 解读

We consider a multivariate time series model which represents a high dimensional vector process as a sum of three terms: a linear regression of some observed regressors, a linear combination of some latent and serially correlated factors, and a vector white noise. We investigate the inference without imposing stationary conditions on the target multivariate time series, the regressors and the underlying factors. Furthermore we deal with the endogeneity that there exist…