LIMIT LAWS FOR LARGE kTH-NEAREST NEIGHBOR BALLS - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2022

LIMIT LAWS FOR LARGE kTH-NEAREST NEIGHBOR BALLS

Norbert Henze
  • Function : Author
  • PersonId : 1130517
Moritz Otto
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  • PersonId : 1130518

Abstract

Let X 1 , X 2 ,. .. , X n be a sequence of independent random points in R d with common Lebesgue density f. Under some conditions on f , we obtain a Poisson limit theorem, as n → ∞, for the number of large probability kth-nearest neighbor balls of X 1 ,. .. , X n. Our result generalizes Theorem 2.2 of [11], which refers to the special case k = 1. Our proof is completely different since it employs the Chen-Stein method instead of the method of moments. Moreover, we obtain a rate of convergence for the Poisson approximation.
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Dates and versions

hal-03611386 , version 1 (17-03-2022)

Identifiers

  • HAL Id : hal-03611386 , version 1

Cite

Nicolas Chenavier, Norbert Henze, Moritz Otto. LIMIT LAWS FOR LARGE kTH-NEAREST NEIGHBOR BALLS. 2022. ⟨hal-03611386⟩
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