On singular values of data matrices with general independent columns
具有一般独立列的数据矩阵的奇异值
We analyze the singular values of a large p×n data matrix Xn=(xn1,…,xnn), where the columns {xnj} are independent p-dimensional vectors, possibly with different distributions. Assuming that the covariance matrices Σnj=Cov(xnj) of the column vectors can be asymptotically simultaneously diagonalized, with appropriately converging spectra, we establish a limiting spectral distribution (LSD) for the singular values of Xn when both dimensions p and n grow to infinity in…