Journal
JOURNAL OF MULTIVARIATE ANALYSIS
Volume 101, Issue 2, Pages 464-475Publisher
ELSEVIER INC
DOI: 10.1016/j.jmva.2009.09.009
Keywords
Common principal components; Eigenfunctions; Functional data analysis; Hilbert-Schmidt operators; Kernel methods; Proportional model
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In many situations, when dealing with several populations with different covariance operators, equality of the operators is assumed. Usually, if this assumption does not hold, one estimates the covariance operator of each group separately, which leads to a large number of parameters. As in the multivariate setting, this is not satisfactory since the covariance operators may exhibit some common structure. In this paper, we discuss the extension to the functional setting of the common principal component model that has been widely studied when dealing with multivariate observations. Moreover, we also consider a proportional model in which the covariance operators are assumed to be equal up to a multiplicative constant. For both models, we present estimators of the unknown parameters and we obtain their asymptotic distribution. A test for equality against proportionality is also considered. (C) 2009 Elsevier Inc. All rights reserved.
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