Before revision:  We show that the limiting empirical spectral distribution of our proposed estimator TVARCV does depend solely on that of Sigma through a Marcenko-Pastur equation, and hence the TVARCV can be used to recover the empirical spectral distribution of Sigma by inverting the Marcenko-Pastur equation, which can then be applied to further applications such as portfolio allocation, risk management, etc. .
After revision:  We show that the limiting empirical spectral distribution of our proposed estimator TVARCV does depend solely on that of the targeting ICV matrix through a Mar\v{c .