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基于 Spearman 相关矩阵的高维因子数稳健估计AI 解读

Determining the number of factors in high-dimensional factor modeling is essential but challenging, especially when the data are heavy-tailed. In this article, we introduce a new estimator based on the spectral properties of Spearman sample correlation matrix under the high-dimensional setting, where both dimension and sample size tend to infinity proportionally. Our estimator is robust against heavy tails in either the common factors or idiosyncratic errors. The consistency…

维数与样本量之比趋于无穷时样本协方差特征值统计量的渐近正态性及应用AI 解读

The asymptotic normality for a large family of eigenvalue statistics of a general sample covariance matrix is derived under the ultrahigh-dimensional setting, that is, when the dimension to sample size ratio p/n→∞. Based on this CLT result, we extend the covariance matrix test problem to the new ultra-high-dimensional context, and apply it to test a matrix-valued white noise. Simulation experiments are conducted for the investigation of finite-sample properties of the…