A0978
Title: Optimal false discovery control of minimax estimators
Authors: Qifan Song - Purdue University (United States) [presenting]
Abstract: Two major research tasks lie at the heart of high-dimensional data analysis: accurate parameter estimation and correct support recovery. The existing literature mostly aims for either the best parameter estimation or the best model selection result. However, little has been done to understand the potential interaction between the estimation precision and the selection behaviour. The minimax result shows that an estimator's type I error control performance directly links with its $L_2$ estimation error rate and reveals a trade-off phenomenon between the rate of convergence and the false discovery control: to achieve better accuracy, one risks yielding more false discoveries. In particular, the false discovery control behaviour of rate optimal and rate suboptimal estimators under different sparsity regimes are characterized, and a rigid dichotomy is discovered between these two estimators under near-linear and linear sparsity settings. In addition, a rigorous explanation is provided for the incompatibility phenomenon between selection consistency and rate minimaxity, which has been frequently observed in the high-dimensional literature.
