Geodesically convex $M$-estimation in metric spaces

Victor-Emmanuel Brunel

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arXiv · 2305.03215

Geodesically convex $M$-estimation in metric spaces

Victor-Emmanuel Brunel

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Abstract

We study the asymptotic properties of geodesically convex $M$-estimation on non-linear spaces. Namely, we prove that under very minimal assumptions besides geodesic convexity of the cost function, one can obtain consistency and asymptotic normality, which are fundamental properties in statistical inference. Our results extend the Euclidean theory of convex $M$-estimation; They also generalize limit theorems on non-linear spaces which, essentially, were only known for barycenters, allowing to consider robust alternatives that are defined through non-smooth $M$-estimation procedures.

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Victor-Emmanuel Brunel. 2023-05-05. Geodesically convex $M$-estimation in metric spaces. https://arxiv.org/abs/2305.03215

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