Before revision:  Hence in terms of making inference about the spectrum of the integrated covariance matrix, the RCV is in generalnot a good proxy to rely on in the high dimensional caseenko-Pastur type theorem for weighted sample covariance matrices, based on which we further establish a Mar\v{c}enko-Pastur type theorem for RCV matrices for a class \mathcal{C} of diffusion processes.
After revision:  Hence in terms of making inference about the spectrum of the integrated covariance matrix, the RCV is in general a good proxy to rely on in the high dimensional caseenko-Pastur type theorem for weighted sample covariance matrices, based on which we further establish a Mar\v{c}enko-Pastur type theorem for RCV matrices for a class \mathcal{C} of diffusion processes.