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Article Dans Une Revue Journal of Applied Probability Année : 2018

Convergence rates for estimators of geodesic distances and Fréchet expectations

Résumé

Consider a sample Xn = {X1 ,. .. , X n } of i.i.d variables drawn with a probability distribution P supported on a set M ⊂ R d. This article mainly deals with the study of a natural estimator for the geodesic distance on M. Under rather general geometric assumptions on M , a general convergence result is proved. Assuming M to be a man-ifold of known dimension d ≤ d, and under regularity assumptions on P X , an explicit convergence rate is given. In the case when M has no boundary, the knwoldege of the dimension d is unnecessary to obtain this convergence rate. The second part of the work consists in building an estimator for the Fréchet expectations on M , and proving its convergence under regularity conditions, applying the previous results.
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Dates et versions

hal-01564166 , version 1 (18-07-2017)
hal-01564166 , version 2 (22-03-2018)

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  • HAL Id : hal-01564166 , version 2

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Catherine Aaron, Olivier Bodart. Convergence rates for estimators of geodesic distances and Fréchet expectations. Journal of Applied Probability, 2018. ⟨hal-01564166v2⟩
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