Hierarchically nested factor model from multivariate data

TL;DR

This paper introduces a hierarchically nested factor model derived from multivariate data, linking hierarchical clustering to correlation structures, and employs bootstrap methods to identify statistically robust factors.

Contribution

It presents a novel hierarchical factor model framework that connects clustering results with correlation matrices and introduces a bootstrap approach for factor selection.

Findings

Hierarchically nested factor model accurately describes multivariate data structure.

Bootstrap procedure effectively reduces the number of significant factors.

Model captures hierarchical relationships in correlation data.

Abstract

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.