On the Symmetry of Limiting Distributions of M-estimators

Arunav Bhowmick; Arun Kumar Kuchibhotla

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arXiv · 2411.17087

On the Symmetry of Limiting Distributions of M-estimators

Arunav Bhowmick·Arun Kumar Kuchibhotla

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Abstract

Many functionals of interest in statistics and machine learning can be written as minimizers of expected loss functions. Such functionals are called $M$-estimands, and can be estimated by $M$-estimators -- minimizers of empirical average losses. Traditionally, statistical inference (e.g., hypothesis tests and confidence sets) for $M$-estimands is obtained by proving asymptotic normality of $M$-estimators centered at the target. However, asymptotic normality is only one of several possible limiting distributions and (asymptotically) valid inference becomes significantly difficult with non-normal limits. In this paper, we provide conditions for the symmetry of three general classes of limiting distributions, enabling inference using HulC (Kuchibhotla et al. (2024)).

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Arunav Bhowmick, Arun Kumar Kuchibhotla. 2024-11-26. On the Symmetry of Limiting Distributions of M-estimators. https://arxiv.org/abs/2411.17087

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