Approximation stochastique en analyse factorielle multiple

Jean-Marie Monnez (1)

1 IECN - Institut Élie Cartan de Nancy

We study the multiple factorial analysis of a random vector X in ℝ^{p} as a principal component analysis of X with a particular choice of the inner product in ℝ^{p}. We use a stochastic approximation process to estimate recursively the principal components of this analysis by means of a sequence of i.i.d. observations of X. Stochastic approximations of the symmetrical positive definite matrix M defining the inner product in ℝ^{p} and of the principal components are made simultaneously.

Mots clés: Principal component analysis; Stochastic approximation; Principal component analysis.

Domaines: Statistiques [math.ST]

Jean-Marie Monnez. Approximation stochastique en analyse factorielle multiple. Publications de l'Institut de Statistique de l'Université de Paris, 2006, L (3), pp.27-45. ⟨hal-00142473⟩