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Lois limites des écarts extrêmes associés aux histogrammes et à diverses statistiques d'ordre dans l'estimation d'une densité de probabilité

Abstract : This work is associated with limit laws problems, coming from a n-size sample (X1,..,Xn) valued into Rs. Chapter 1 is dedicated to multinomial law aspects, and brings limit laws for extreme values related to occupancy problems. Some results from P.Revesz (1971-72) are significantly improved, leading to limit laws for density estimation upon Rs, using two methods called random histogram density estimation. Chapter 2 is dedicated to joint law analysis for inter-quantile spreads, and leads to a new limit law for extreme values of those spreads, generalizing G.Tusnady's (1974) work on the subject. Chapter 3 goes further down Tusnady's work on density estimation using random histograms. An asymptotically poissonnian character of both multinomial and Dirichlet laws is demonstrated, under very general hypothesis.
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https://tel.archives-ouvertes.fr/tel-00751542
Contributor : Michel Bera <>
Submitted on : Tuesday, November 13, 2012 - 6:18:14 PM
Last modification on : Friday, May 29, 2020 - 3:57:13 PM
Long-term archiving on: : Thursday, February 14, 2013 - 3:43:20 AM

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  • HAL Id : tel-00751542, version 1

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Michel Béra. Lois limites des écarts extrêmes associés aux histogrammes et à diverses statistiques d'ordre dans l'estimation d'une densité de probabilité. Statistiques [math.ST]. Université Pierre et Marie Curie - Paris VI, 1977. Français. ⟨tel-00751542⟩

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