The application of spectral distribution of product of two random matrices in the factor analysis

In the factor analysis model with large cross-section and time-series dimensions,we pro- pose a new method to estimate the number of factors.Specially if the idiosyncratic terms satisfy a linear time series model,the estimators of the parameters can be obtained in the time series model. The theoretical properties of the estimators are also explored.A simulation study and an empirical analysis are conducted.

The convergence on spectrum of sample covariance matrices for information-plus-noise type data

In this paper,we consider the limiting spectral distribution of the information-plus-noise type sample covariance matrices Cn=1/N（Rn＋σXn）（Rn＋σXn）,under the assumption that the entries of Xn are independent but non-identically distributed random variables.It is proved that,almost surely,the empirical spectral distribution of Cn converges weakly to a non-random distribution whose Stieltjes transform satisfies a certain equation.Our result extends the previous one with the entries of Xn are i.i.d.random varibles to a more general case.The proof of the result mainly employs the Stein equation and the cumulant expansion formula of independent random variables.

On eigenvalues of a high-dimensional Kendall's rank correlation matrix with dependence

In this paper,we investigate the limiting spectral distribution of a high-dimensional Kendall’s rank correlation matrix.The underlying population is allowed to have a general dependence structure.The result no longer follows the generalized Marcenko-Pastur law,which is brand new.It is the first result on rank correlation matrices with dependence.As applications,we study Kendall’s rank correlation matrix for multivariate normal distributions with a general covariance matrix.From these results,we further gain insights into Kendall’s rank correlation matrix and its connections with the sample covariance/correlation matrix.