Set Estimation from Projected Multidimensional Random Variables with Application to a Discrete-Time Skorokhod Problem - MODAL'X - UMR 9023 - Modélisation aléatoire de Paris Nanterre
Pré-Publication, Document De Travail Année : 2024

Set Estimation from Projected Multidimensional Random Variables with Application to a Discrete-Time Skorokhod Problem

Nicolas Marie

Résumé

This paper deals with sufficient conditions on the distribution of the random variable $H$, in the model $X =\Pi_C(H)$, for the convex hull $\widehat C_N$ of $N$ independent copies of $X$ to be a consistent estimator - with or without rate of convergence - of the convex body $C$. The convergence of $\widehat C_N$ is established for the Hausdorff distance under uniform conditions on the distribution of $H$, but also in a pointwise sense under less demanding conditions. Some of these convergence results on $\widehat C_N$ are applied to the estimation of the time-dependent constraint set involved in a discrete-time Skorokhod problem.
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Dates et versions

hal-04637441 , version 1 (06-07-2024)
hal-04637441 , version 2 (29-08-2024)

Identifiants

  • HAL Id : hal-04637441 , version 2

Citer

Nicolas Marie. Set Estimation from Projected Multidimensional Random Variables with Application to a Discrete-Time Skorokhod Problem. 2024. ⟨hal-04637441v2⟩
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