High-dimensional robust principal component analysis and its applications

Principal component analysis method is one of the most widely used statistical procedures for data dimension reduction. The traditional principal component analysis method is sensitive to outliers since it is based on the sample covariance matrix. Meanwhile, the deviation of the principal component analysis based on the Minimum Covariance Determinant (MCD) estimation is significantly increased as the data dimension increases. In this paper, we propose a high-dimensional robust principal component analysis based on the Rocke estimator. Simulation studies and a real data analysis illustrate that the finite sample performance of the proposed method is significantly better than those of the existing methods.