Robust Estimation for Factor Models Based on Modiffed Huber Loss
Description
Our research is about robust analysis for high dimensional factor model in present of heavy-tailed data. We propose novel methods by integrate the modified Huber loss function and the common Principal Component Analysis. The methods are superior or comparable to others in numerical studies and the estimated factor number is more aligned with financial practice. The real data in finance is from Kenneth R. French's website: http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html. We use three portfolio pools: Pool A, Pool B, and Pool C to do factor analysis. Each pool contains 100 portfolios with complete monthly average value-weighted returns data from July 2016 to June 2024. The Portfolios in each pool are influenced by two primary factors. The authors have no permission to share the data or make the data public available. We give the R codes for data generating, parameter setting and computational details in simulations.