ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

12. Probability and Statistics

1991 MS Classification: 62G07 Jähnisch, Michael, Weierstrass Institute Berlin Asymptotic equivalence for a density model with independent but non identically distributed random variables We consider the following nonparametric model:

Y_{1}, ..., Y_{n} ∈ [0, 1]

are independent observations with densities

Y_{i} ∼ h(i/n, .) h ∈ Σ

Where Σ is contained in a Hölder ball of radius C. The goal is to find a sequence of Gaussian experiments that approximates our model in the sense of the Le Cam Δ-distance. The main tool to achieve this is a functional version of the strong approximation of the sequential empirical process by the Kiefer process.