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- W4241580656 abstract "In 1975, Komlós, Major and Tusnády constructed a strong approximation of the uniform empirical process αn(t),n ≥ 1, t ε [0.1] by a Gaussian Kiefer process. We show that the global error bound provided by Komlós, Major and Tusnády may be improved by considering only local approximation. Moreover we provide explicit constants. We also prove a local refinement for Tusnády's Gaussian strong approximation of the bidimensional uniform empirical process. The main technical tool we use is a non asymptotic normal approximation of the hypergeometric distribution.En 1975, Komlós, Major et Tusnády ont réalisé l'approximation forte du processus empirique uniforme αn(t), n ≥ 1, t ε [0.1] par un processus gaussien de Kiefer. Nous montrons que la borne d'erreur globale donnée par Komlós, Major et Tusnády peut être améliorée si l'on ne considère que l'approximation locale. De plus nous donnons des constantes explicites. Nous établissons également une amélioration locale de l'approximation forte gaussienne du processus empirique uniforme bidimensionnel dûe à Tusnady. Le principal outil technique utilisé est l'approximation normale non asymptotique de la loi hypergéométrique." @default.
- W4241580656 created "2022-05-12" @default.
- W4241580656 date "2002-10-01" @default.
- W4241580656 modified "2023-10-14" @default.
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- W4241580656 doi "https://doi.org/10.1016/s0378-4320(02)00178-1" @default.
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