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Article Dans Une Revue Complex Analysis and Operator Theory Année : 2008

Local functional principal component analysis

Résumé

Covariance operators of random functions are crucial tools to study the way random elements concentrate over their support. The principal component analysis of a random function X is well-known from a theoretical viewpoint and extensively used in practical situations. In this work we focus on local covariance operators. They provide some pieces of information about the distribution of X around a fixed point of the space x₀. A description of the asymptotic behaviour of the theoretical and empirical counterparts is carried out. Asymptotic developments are given under assumptions on the location of x₀ and on the distributions of projections of the data on the eigenspaces of the (non-local) covariance operator.
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Dates et versions

hal-00132368 , version 1 (21-02-2007)

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André Mas. Local functional principal component analysis. Complex Analysis and Operator Theory, 2008, 2, pp.135-167. ⟨10.1007/s11785-007-0026-x⟩. ⟨hal-00132368⟩
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