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

TL;DR

This paper demonstrates that a simple data-dependent measure can achieve optimal inference, accurate estimation, reliable structure learning, and computational efficiency in high-dimensional sparse sequence models.

Contribution

It introduces a straightforward data-dependent measure that attains optimal inference and robustness in sparse sequence models, balancing accuracy and computational scalability.

Findings

Achieves asymptotically optimal inference in sparse models.

Provides robustness to error distribution variations.

Maintains computational efficiency in high dimensions.

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.