@article {4990,
	title = {Identifying the spectral representation of Hilbertian time series},
	journal = {Statistics \& Probability Letters},
	volume = {118},
	year = {2016},
	pages = {45-49},
	abstract = {<p>We provide √n-consistency results regarding estimation of the spectral representation of covariance operators of Hilbertian time series, in a setting with imperfect measurements. This is a generalization of the method developed in Bathia et al. (2010). The generalization relies on an important property of centered random elements in a separable Hilbert space, namely, that they lie almost surely in the closed linear span of the associated covariance operator. We provide a straightforward proof to this fact. This result is, to our knowledge, overlooked in the literature. It incidentally gives a rigorous formulation of Principal Component Analysis in Hilbert spaces.</p>
},
	author = {Horta, Eduardo and Flavio Ziegelmann}
}
