关键词: 高维成分数据, 近似零值, Lasso-分位回归, 修正EM算法, 稳健

Abstract: High-dimensional compositional data with massive rounded zeros and missing values are arising with the fast development of computer technology and bring much challenge to traditional statistical methods. The thick-tail and complicated covariance structure make the analysis even more difficult, thus exploring robust methods for imputation of rounded zeros in high-dimensional compositional data becomes the current focus of academic research. To this end, a robust method (SubLQR) based on modified EM algorithm is proposed, combining R-type clustering and Lasso-Quantile regression. The proposed SubLQR is superior to the existing imputation methods in the following aspects: 1) Robustness: with the application of Lasso-Quantile regression, a sparse pattern is provided; 2) Efficiency: with the use of R-type clustering, computation cost is reduced and precision is improved. Simulation results suggest that the proposed method performs better than the existing methods, especially when the percentage of zeros and outliners is large. Finally, real data analysis in metabolomics study of rare disease indicates the wide applicability of the proposed SubLQR.

Key words: High-dimensional Compositional Data, Rounded Zeros, Lasso-Quantile Regression, Modified EM Algorithm, Robustness