<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Horta, Eduardo</style></author><author><style face="normal" font="default" size="100%">Flavio Ziegelmann</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Identifying the spectral representation of Hilbertian time series</style></title><secondary-title><style face="normal" font="default" size="100%">Statistics &amp; Probability Letters</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2016</style></year></dates><volume><style face="normal" font="default" size="100%">118</style></volume><pages><style face="normal" font="default" size="100%">45-49</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;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.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">November 2016</style></issue></record></records></xml>