| Abstract |
In this talk, we will discuss the discrete argmin inference problem in high-dimensional settings. Given n observations from a d dimensional vector, the goal is to test whether the rth component of the mean vector is the smallest among all components. We propose dimension-agnostic tests that maintain validity regardless of how d scales with n, and regardless of arbitrary ties in the mean vector. Notably, our validity holds under mild moment conditions, requiring little more than finiteness of a second moment, and permitting possibly strong dependence between coordinates. In addition, we establish the local minimax separation rate for this problem, which adapts to the cardinality of a confusion set, and show that the proposed tests attain this rate. Empirical results illustrate the strong performance of our approach in terms of type I error control and power compared to existing methods. |
