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Weak convergence of an empirical process indexed by the closed convex subsets ofI 2

Authors:	Erwin Bolthausen

Institution:	(1) Fachgruppe Statistik, Universität Konstanz, D-7750 Konstanz

Abstract:	Summary LetI ² be the unit cube of $\mathbb{R}^2$ andX _i be independentI ²-valued random variables that are distributed according to Lebesgue-measure. IfS is the set of closed convex subsets ofI ² we consider the process _n (A) _AS,where $\mu _n (A) = (1/n)\mathop \sum \limits^n 1{}_A(X_i ).$ .It is proved that this process suitably normalized converges in a suitable weak sense to a Gaussian process.

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