Rotation to Sparse Loadings using L^p Functions

Exploratory factor analysis is a probabilistic dimension reducing technique highly popular in social and behavioral science. Typically, the interest lies in finding sparse loading structures. The focus of this talk is on the rotation method that is traditionally used for solving this kind of problem and its connection to regularized estimation will be explained.

We propose a family of loss functions, the component-wise L^p loss, as the rotation criterion, which is a special case of the concave component-wise loss functions. The advantage, estimator’s statistical consistency, and computation of this method will be discussed in this talk.