Before revision:  As in the case of a simple kernel estimator of spot volatility in the absence of microstructure noise, we show that the asymptotic variance of the pre-averaging/kernel estimator  is minimal for exponential or Laplace kernels, hence, justifying the need of working with unbounded kernels as proposed in this work.
After revision:  As in the case of a simple kernel estimator of spot volatility in the absence of microstructure noise, we show that the asymptotic variance of the pre-averaging/kernel estimator is minimal for exponential or Laplace kernels, hence, justifying the need of working with kernels of unbounded support as proposed in this work.