Weak convergence of an empirical process indexed by the closed convex subsets ofI 2期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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

Authors:	Erwin Bolthausen

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

Abstract:	Summary LetI² be the unit cube of $mathbb{R}^2$ andX_i be independentI²-valued random variables that are distributed according to Lebesgue-measure. IfS is the set of closed convex subsets ofI² 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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