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高维张量时间序列的 CP 因子分解与双投影迭代AI 解读

We adopt the canonical polyadic (CP) decomposition to model high-dimensional tensor time series. Our primary goal is to identify and estimate the factor loadings in the CP decomposition. We propose a one-pass estimation procedure through standard eigen-analysis for a matrix constructed based on the serial dependence structure of the data. The asymptotic properties of the proposed estimator are established under a general setting as long as the factor loading vectors are…

通过惩罚最小二乘实现一步式分组因子分析AI 解读

In this article, we revisit the problem of group factor analysis and propose a one-step penalized least squares method to estimate the factor loadings and factors in large-dimensional group factor models, offering a distinct alternative to the conventional two-step principal component approach. Our procedure originates from the equivalence between the group factor structure and the carefully tailored identification conditions. Leveraging this insight, we develop a tricky…

矩阵值椭圆分布观测的新非参数 Kendall 秩相关方法AI 解读

In this article, we first propose generalized row/column matrix Kendall's tau for matrix-variate observations that are ubiquitous in areas such as finance and medical imaging. For a random matrix following a matrix-variate elliptically contoured distribution, we show that the eigenspaces of the proposed row/column matrix Kendall's tau coincide with those of the row/column scatter matrix respectively, with the same descending order of the eigenvalues. We perform eigenvalue…

矩阵分位数因子模型AI 解读

This paper introduces a matrix quantile factor model for matrix-valued data with low-rank structure. We estimate the row and column factor spaces via minimizing the empirical check loss function with orthogonal rotation constraints. We show that the estimates converge at rate $(\min\{p_1p_2,p_2T,p_1T\})^{-1/2}$ in the average Frobenius norm, where $p_1$, $p_2$ and $T$ are the row dimensionality, column dimensionality and length of the matrix sequence, respectively. This rate…

利用自助样本协方差矩阵检验高维因子模型的共同因子数AI 解读

This paper studies the impact of bootstrap procedure on the eigenvalue distributions of the sample covariance matrix under a high-dimensional factor structure. We provide asymptotic distributions for the top eigenvalues of bootstrapped sample covariance matrix under mild conditions. After bootstrap, the spiked eigenvalues which are driven by common factors will converge weakly to Gaussian limits after proper scaling and centralization. However, the largest non-spiked…

广义椭圆模型下样本协方差矩阵的极端特征值及应用AI 解读

We consider the extreme eigenvalues of the sample covariance matrix $Q=YY^*$ under the generalized elliptical model that $Y=Σ^{1/2}XD.$ Here $Σ$ is a bounded $p \times p$ positive definite deterministic matrix representing the population covariance structure, $X$ is a $p \times n$ random matrix containing either independent columns sampled from the unit sphere in $\mathbb{R}^p$ or i.i.d. centered entries with variance $n^{-1},$ and $D$ is a diagonal random matrix containing…

矩阵因子分析：从最小二乘到迭代投影AI 解读

In this article, we study large-dimensional matrix factor models and estimate the factor loading matrices and factor score matrix by minimizing square loss function. Interestingly, the resultant estimators coincide with the Projected Estimators (PE) in Yu et al.(2022), which was proposed from the perspective of simultaneous reduction of the dimensionality and the magnitudes of the idiosyncratic error matrix. In other word, we provide a least-square interpretation of the PE…

矩阵序列应采用单向还是双向因子模型？AI 解读

This paper investigates the issue of determining the dimensions of row and column factor spaces in matrix-valued data. Exploiting the eigen-gap in the spectrum of sample second moment matrices of the data, we propose a family of randomised tests to check whether a one-way or two-way factor structure exists or not. Our tests do not require any arbitrary thresholding on the eigenvalues, and can be applied with no restrictions on the relative rate of divergence of the…

潜在双向因子结构下矩阵时间序列的在线变点检测AI 解读

This paper proposes a novel methodology for the online detection of changepoints in the factor structure of large matrix time series. Our approach is based on the well-known fact that, in the presence of a changepoint, a factor model can be rewritten as a model with a larger number of common factors. In turn, this entails that, in the presence of a changepoint, the number of spiked eigenvalues in the second moment matrix of the data increases. Based on this, we propose two…