Kernel estimate of spectral density functions of sample covariance matrices with relaxed independence conditions

Abstract

We focus on kernel estimator of the density function of the limiting spectral distribution of sample covariance matrix associated firstly, to a large class of weak dependent sequences of real-valued random variables having only moment of order 2. Afterwards, sample covariance matrices of the block-independent model and the random tensor model, where the data does not have independent coordinates. In the two last cases, we show that the kernel estimator of the density function converges with probability one to the Marchenko-Pastur density. A simulation study is conducted to show the performance of the kernel estimators of the density function and then compare these estimators with the one obtained by the Stieltjes transform method.