Before revision:  Several examples of LPE , in which the conditions are shown to be satisfied assuming that the microstructure noise is O_p(1/\sqrt{n : estimation of volatility, powers of volatility, high-frequency covariance and volatility when incorporating trading information . The LPE considered in those cases are variations of the maximum likelihood estimator. We also treat the case of time-varying model with uncertainty zones and the time-varying MA(1).
After revision:  Several examples of LPE , in which the conditions are shown to be satisfied assuming that the microstructure noise is O_p(1/\sqrt{n : estimation of volatility, powers of volatility, high-frequency covariance and volatility when incorporating trading information and time-varying MA(1).