Title: Sparse factor models: Asymptotic properties
Authors: Benjamin Poignard - Osaka University (Japan) [presenting]
Yoshikazu Terada - Osaka University; RIKEN (Japan)
Abstract: The problem of estimating a factor model-based variance-covariance matrix is considered when the factor loading matrix is assumed sparse. We develop a penalised $Z$-estimation framework to handle the identifiability issue of the factor loading matrix while fostering sparsity in potentially all its entries. We prove the oracle property of the penalised $Z$-estimator for the factor model; that is, the penalisation procedure can recover the true sparse support, and the estimator is asymptotically normally distributed. The non-penalised loss functions are deduced from the class of Bregman divergence losses, providing new estimators for factor modelling. Empirical studies support these theoretical results.