  In this paper, we study the Edgeworth expansion for a pre-averaging estimator
of quadratic variation in the framework of continuous diffusion models observed
with noise. More specifically, we obtain a second order expansion for the joint
density of the estimators of quadratic variation and its asymptotic variance.
Our approach is based on martingale embedding, Malliavin calculus and stable
central limit theorems for continuous diffusions. Moreover, we derive the
density expansion for the studentized statistic, which might be applied to
construct asymptotic confidence regions.
