[Statlist] Séminaire Institut de Statistique, 20/11/2007

[ISTAT Messagerie]

SEMINAIRE DE STATISTIQUE
Institut de Statistique, Université de Neuchâtel 
Pierre à Mazel 7 (1er étage,salle 110), Neuchâtel,
http://www2.unine.ch/statistics

Mardi 20 novembre 2007, 11h00
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Ludovic Lebart (ENST, Paris)

Resampling techniques for assessing the visualisations of multivariate data 

Multivariate descriptive  techniques involving singular values decomposition  such as Principal Components Analysis, Simple and Multiple Correspondence analysis) may provide misleading visualisations of the data. We briefly show that several types of resampling techniques could be carried out to assess the quality of the obtained visualisations: a) Partial bootstrap, that considers the replications as supplementary variables, without diagonalization of the replicated moment-product matrices. b) Total bootstrap type 1, that performs a new diagonalization for each replicate, with corrections limited to possible changes of signs of the axes. c) Total bootsrap type 2, which adds to the preceding one a correction for the possible exchanges of axes. d) Total bootstrap type 3, that implies procrustean transformations of all the replicates striving to take into account both rotations and exchanges of axes. e) Specific bootstrap, implying a resampling at different levels (case of a hierarchy of statistical units). Examples are presented and discussed for each technique.