Thursday, July 3, 2025 - 16:15 in U2-232
Some estimators of location in a finite metric tree
A talk in the Oberseminar Probability Theory and Mathematical Statistics series by
Gabriel Romon from University of Luxembourg
| Abstract: |
During this talk we discuss parameters of central tendency for a population on a network, which is modeled by a finite metric tree.
In this non-Euclidean setting, we develop location parameters called generalized Fréchet means, which are obtained by replacing the usual objective function $\alpha \mapsto \operatorname{E}[d(\alpha,X)^2]$ with $\alpha \mapsto \operatorname{E}[\ell(d(\alpha,X))]$, where $\ell$ is a generic convex nondecreasing loss function.
We develop a notion of directional derivative in the tree, which helps up locate and characterize the minimizers. Estimation is performed using a sample analog.
We extend to a finite metric tree the so-called notion of "stickiness", we show that this phenomenon has a non-asymptotic component and we present a sticky law of large numbers.
For the particular cases of the Fréchet mean and the Fréchet median, we develop non-asymptotic concentration bounds and sticky central limit theorems.
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