Weak convergence of discretely observed functional data with applications

JOURNAL OF MULTIVARIATE ANALYSIS

卷:146

Article

Nagy, Stanislav^1,2,3  Gijbels, Irene^1,2  Hlubinka, Daniel³ 

[1] Katholieke Univ Leuven, Dept Math, Stat Sect, Celestijnenlaan 200b Box 2400, B-3001 Leuven, Belgium

[2] Katholieke Univ Leuven, Leuven Stat Res Ctr LStat, Celestijnenlaan 200b Box 5307, B-3001 Leuven, Belgium

[3] Charles Univ Prague, Dept Probabil & Math Stat, Sokolovska 83, Prague 18675 8, Czech Republic

关键词: Consistency;    Data depth;    Functional data;    Functional moments;    Weak convergence;   

DOI  :  10.1016/j.jmva.2015.06.006

来源: Elsevier

【 摘 要 】

A general result on weak convergence of the empirical measure of discretely observed functional data is shown. It is applied to the problem of estimation of functional mean value, and the problem of consistency of various types of depth for functional data. Counterexamples illustrating the fact that the assumptions as stated cannot be dropped easily are given. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free