Folded‐Concave Dantzig Selector and Inference for High‐Dimensional Partial Log‐Contrast Models

ABSTRACT Recent advances in high‐throughput sequencing technology development have led to a huge demand for statistical methods for analyses of massive compositional data. Investigation of specific components of the composition that are associated with an outcome of interest can sometimes provide invaluable insights in biomedical research. Unfortunately, both the compositional nature and high dimensionality pose grand challenges for statistical analyses on this task. In the literature of high‐dimensional statistics, the Dantzig selector is widely used for variable selection in ultra‐high‐dimensional data. To incorporate the compositional nature of the data, we propose a partially penalized compositional Dantzig selector (PPC‐DS) to identify outcome‐associated components of a compositional predictor. An efficient computing algorithm is developed to calculate our PPC‐DS estimator. By leaving the components of interest unpenalized in PPC‐DS, we further propose statistical inference procedures for these components in our PPC‐DS estimator. Numerical simulations are conducted to evaluate the performance of PPC‐DS and its potential usefulness is further illustrated via a