GENERALIZED THRESHOLDING ESTIMATORS FOR HIGH-DIMENSIONAL LOCATION PARAMETERS

Analyzing high-throughput genomic, proteomic, and metabolomic data usually involves estimating high-dimensional location parameters. Thresholding es- timators can significantly improve such estimation when many parameters are zero, i.e., parameters are sparse. Several such estimators have been constructed to be adaptive to parameter sparsity. However, they assume that the underlying param- eter spaces are symmetric. Since many applications present asymmetry parameter spaces, we introduce a class of generalized thresholding estimators. A construc- tion of these estimators is developed using a Bayes approach, where an important constraint on the hyperparameters is identified. A generalized empirical Bayes im- plementation is presented for estimating high-dimensional yet sparse normal means. This implementation provides generalized thresholding estimators which are adap- tive to both sparsity and asymmetry of high-dimensional parameters.