Asymptotically optimal inference in sparse sequence models with a simple data-dependent measure

Abstract: For high-dimensional inference problems, statisticians have a number of competing interests. On the one hand, procedures should provide accurate estimation, reliable structure learning, and valid uncertainty quantification. On the other hand, procedures should be computationally efficient and able to scale to very high dimensions. In this note, I show that a very simple data-dependent measure can achieve all of these desirable properties simultaneously, along with some robustness to the error distribution, in sparse sequence models.