Discovering Common Structures Across High-Dimensional Factor Models

Music City Center 

A sequential testing procedure is proposed to uncover common structures across multiple high-dimensional factor models. The test is motivated by observing data from multiple individuals, which can be modeled through factor models that potentially share information encoded in their respective loading matrices. The introduced sequential procedure allows testing whether these loading matrices are identical up to a rotational change or if only a partial set of column vectors is shared across individuals. The theoretical results cover the asymptotic behavior of the test statistic, supported by a simulation study demonstrating promising empirical test size and power. Finally, the method is applied to investigate the relationship between multiple individuals with anxiety disorder.

Common structures, Sequential testing, High-dimensional factor models.