Consistency of non-integrated depths for functional data

JOURNAL OF MULTIVARIATE ANALYSIS

卷:140

Article

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

[1] Katholieke Univ Leuven, Dept Math, Stat Sect, B-3001 Leuven, Belgium

[2] Katholieke Univ Leuven, Leuven Stat Res Ctr LStat, B-3001 Leuven, Belgium

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

关键词: Band depth;    Functional data;    Glivenko-Cantelli theorem;    Half-region depth;    Infimal depth;    Uniform consistency;   

DOI  :  10.1016/j.jmva.2015.05.012

来源: Elsevier

【 摘 要 】

In the analysis of functional data, the concept of data depth is of importance. Strong consistency of a sample version of a data depth is among the basic statistical properties that need to hold. In this paper we discuss consistency properties of three popular types of functional depth: the band depth, the half-region depth and the infimal depth. The latter is a special case of the recently introduced general class of Phi-depths. All three considered depth functions are of a non-integrated type. Counterexamples illustrate some problems with consistency results for these data depths. The main contribution of this paper consists of providing sufficient conditions for consistency of these non-integrated data depths to hold. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free