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What is Learnable in Valiant's Theory of the Learnable? 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On the asymptotic normality of kernel estimators of the long run covariance of functional time series
István Berkes, Lajos Horváth, Gregory Rice · 2015-03-03 · via math.ST updates on arXiv.org

We consider the asymptotic normality in $L^2$ of kernel estimators of the long run covariance kernel of stationary functional time series. Our results are established assuming a weakly dependent Bernoulli shift structure for the underlying observations, which contains most stationary functional time series models, under mild conditions. As a corollary, we obtain joint asymptotics for functional principal components computed from empirical long run covariance operators, showing that they have the favorable property of being asymptotically independent.

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