  This paper presents the nonparametric inference for nonlinear volatility
functionals of general multivariate It\^o semimartingales, in high-frequency
and noisy setting. Pre-averaging and truncation enable simultaneous handling of
noise and jumps. Second-order expansion reveals explicit biases and a pathway
to bias correction. Estimators based on this framework achieve the optimal
convergence rate. A class of stable central limit theorems are attained with
estimable asymptotic covariance matrices. This paper form a basis for infill
asymptotic results of, for example, the realized Laplace transform, the
realized principal component analysis, the continuous-time linear regression,
and the generalized method of integrated moments, hence helps to extend the
application scopes to more frequently sampled noisy data.
