Geodesic
Statistical Estimation of Generalized Dimensions
Matematičeskie zametki, Tome 71 (2002) no. 5, pp. 697-712

Voir la notice de l'article provenant de la source Math-Net.Ru

A statistical estimate for generalized dimensions of a set $A\subset \mathbb R^m$ based on the computation of average distances to the closest points in a sample of elements of A is given. For smooth manifolds with Lebesgue measures and for self-similar fractals with self-similar measures, the estimate is proved to be consistent. 
@article{MZM_2002_71_5_a5,
     author = {V. V. Maiorov and E. A. Timofeev},
     title = {Statistical {Estimation} of {Generalized} {Dimensions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {697--712},
     publisher = {mathdoc},
     volume = {71},
     number = {5},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2002_71_5_a5/}
}
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V. V. Maiorov; E. A. Timofeev. Statistical Estimation of Generalized Dimensions. Matematičeskie zametki, Tome 71 (2002) no. 5, pp. 697-712. http://geodesic.mathdoc.fr/item/MZM_2002_71_5_a5/