  We show how to achieve a statistical description of the hierarchical
structure of a multivariate data set. Specifically we show that the similarity
matrix resulting from a hierarchical clustering procedure is the correlation
matrix of a factor model, the hierarchically nested factor model. In this
model, factors are mutually independent and hierarchically organized. Finally,
we use a bootstrap based procedure to reduce the number of factors in the model
with the aim of retaining only those factors significantly robust with respect
to the statistical uncertainty due to the finite length of data records.
