  This paper proposes sparse and easy-to-interpret proximate factors to
approximate statistical latent factors. Latent factors in a large-dimensional
factor model can be estimated by principal component analysis (PCA), but are
usually hard to interpret. We obtain proximate factors that are easier to
interpret by shrinking the PCA factor weights and setting them to zero except
for the largest absolute ones. We show that proximate factors constructed with
only 5-10% of the data are usually sufficient to almost perfectly replicate the
population and PCA factors without actually assuming a sparse structure in the
weights or loadings. Using extreme value theory we explain why sparse proximate
factors can be substitutes for non-sparse PCA factors. We derive analytical
asymptotic bounds for the correlation of appropriately rotated proximate
factors with the population factors. These bounds provide guidance on how to
construct the proximate factors. In simulations and empirical analyses of
financial portfolio and macroeconomic data we illustrate that sparse proximate
factors are close substitutes for PCA factors with average correlations of
around 97.5% while being interpretable.
