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A0490
Title: On singular values of data matrices with general independent columns Authors:  Tianxing Mei - The University of Hong Kong (Hong Kong)
Chen Wang - University of Hong Kong (Hong Kong) [presenting]
Jeff Yao - The University of Hong Kong (Hong Kong)
Abstract: The focus is on singular values of a large $p\times n$ data matrix $X_n =(x_{n1}, . . . ,x_{nn})$ where the columns $\{x_{nj}\}$ are independent $p$-dimensional vectors, possibly with different distributions. Assuming that the covariance matrices $n_j = Cov(x_{nj})$ of the column vectors can be asymptotically simultaneously diagonalizable, with appropriately converging spectra, we establish a limiting distribution for the singular values of $X_n$ when both dimension $p$ and $n$ grow to infinity in comparable magnitude. The matrix model goes beyond and includes many existing works on different types of sample covariance matrices, such as the weighted sample covariance matrix, the Gram matrix model and the sample covariance matrix of linear times series models. Furthermore, we develop three applications of our general approach. First, we obtain the existence and uniqueness of a new limiting spectral distribution of realized covariance matrices for a multi-dimensional diffusion process with anisotropic time-varying co-volatility processes. Secondly, we derive the limiting spectral distribution for singular values of the data matrix for a recent matrix-valued auto-regressive model. Finally, for a generalized finite mixture model, the limiting spectral distribution for singular values of the data matrix is obtained.