High-dimensional latent panel quantile regression with an application to asset pricing

We propose a generalization of the linear panel quantile regression model to accommodate both sparse and dense parts: means that while number covariates available is large, potentially only much smaller them have nonzero impact on each conditional response variable; part represent by low-rank matrix can be approximated latent factors their loadings. Such structure poses problems for traditional estimators, such as ℓ1-penalized regression, factor estimators PCA. new estimation procedure, based ADMM algorithm, consists combining loss function with ℓ1 nuclear norm regularization. show, under general conditions, our estimator consistently estimate coefficients matrix. This done in challenging setting allows temporal dependence, heavy-tail distributions presence factors. Our proposed has “Characteristics + Latent Factors” Quantile Asset Pricing Model interpretation: we apply large-dimensional financial data find (i) characteristics sparser predictive power once were controlled (ii) at upper lower quantiles are different from median.