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• W2738414335 abstract "Abstract Consider a sample 𝒳 n ={ X 1 ,…, X n } of independent and identically distributed variables drawn with a probability distribution ℙ X supported on a compact set M ⊂ℝ d . In this paper we mainly deal with the study of a natural estimator for the geodesic distance on M . Under rather general geometric assumptions on M , we prove a general convergence result. Assuming M to be a compact manifold of known dimension d ′≤ d , and under regularity assumptions on ℙ X , we give an explicit convergence rate. In the case when M has no boundary, knowledge of the dimension d ′ is not needed 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." @default.
• W2738414335 created "2017-07-31" @default.
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• W2738414335 date "2018-12-01" @default.
• W2738414335 modified "2023-10-17" @default.
• W2738414335 title "Convergence rates for estimators of geodesic distances and Frèchet expectations" @default.
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• W2738414335 doi "https://doi.org/10.1017/jpr.2018.66" @default.
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