Adaptive LASSO regression against heteroscedastic idiosyncratic factors in the covariates

摘要

Recent studies suggest that by including the principal components of the covariates, LASSO regression achieves certain consistency properties when the idiosyncratic factors are homoscedastic. In this paper, it is shown that if the principal components are replaced by the common factors obtained based on the maximum likelihood estimation of factor model and the covariates are replaced by the estimated idiosyncratic factors, selection consistency holds even in the heteroscedestic cases. The new results hold for both LASSO and adaptive LASSO under the high-dimensional settings with p -> infinity but p = o(n), where p and n are the number of components of the covariates and the number of observations respectively. Simulation studies suggest that when the idiosyncratic factors are heteroscedastic, penalized regression based on factor analysis outperforms that based on principal component analysis. To illustrate the ideas, real data examples of international economic input-output data and international stock indexes data are studied in particular.