  The SIML (abbreviation of Separating Information Maximal Likelihood) method,
has been introduced by N. Kunitomo and S. Sato and their collaborators to
estimate the integrated volatility of high-frequency data that is assumed to be
an It\^o process but with so-called microstructure noise. The SIML estimator
turned out to share many properties with the estimator introduced by P.
Malliavin and M.E. Mancino. The present paper establishes the consistency and
the asymptotic normality under a general sampling scheme but without
microstructure noise. Specifically, a fast convergence shown for
Malliavin--Mancino estimator by E. Clement and A. Gloter is also established
for the SIML estimator.
