Inference in latent factor regression with clusterable features

Understand

Regression models, in which the observed features $X \in \R^p$ and the response $Y \in \R$ depend, jointly, on a lower dimensional, unobserved, latent vector $Z \in \R^K$, with $K< p$, are popular in a large array of applications, and mainly used for predicting a response from correlated features.

• In contrast, methodology and theory for inference on the regression coefficient $\beta$ relating $Y$ to $Z$ are scarce, since typically the un-observable factor $Z$ is hard to interpret.
• Furthermore, the determination of the asymptotic variance of an estimator of $\beta$ is a long-standing problem, with solutions known only in a few particular cases.
• To address some of these outstanding questions, we develop inferential tools for $\beta$ in a class of factor regression models in which the observed features are signed mixtures of the latent factors.