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.

翻译：SIML（Separating Information Maximal Likelihood的缩写）方法由N. Kunitomo和S. Sato及其合作者提出，用于估计高频数据的积分波动率，该数据假设为Itô过程但存在所谓的微观结构噪声。SIML估计量被证实与P. Malliavin和M.E. Mancino提出的估计量具有许多共同性质。本文在一般抽样方案下且无微观结构噪声时，建立了该估计量的一致性和渐近正态性。具体而言，E. Clement和A. Gloter针对Malliavin–Mancino估计量证明的快速收敛性，本文亦为SIML估计量建立了该性质。