Bridging Root-$n$ and Non-standard Asymptotics: Dimension-agnostic Adaptive Inference in M-Estimation

Kenta Takatsu and Arun Kumar Kuchibhotla

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Abstract: This manuscript studies a general approach to construct confidence sets for the solution of population-level optimization, commonly referred to as M-estimation. Statistical inference for M-estimation poses significant challenges due to the non-standard limiting behaviors of the corresponding estimator, which arise in settings with increasing dimension of parameters, non-smooth objectives, or constraints. We propose a simple and unified method that guarantees validity in both regular and irregular cases. Moreover, we provide a comprehensive width analysis of the proposed confidence set, showing that the convergence rate of the diameter is adaptive to the unknown degree of instance-specific regularity. We apply the proposed method to several high-dimensional and irregular statistical problems.

Date: 2025-01, Revised 2025-02
New Economics Papers: this item is included in nep-ecm
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