Influence function of projection-pursuit principal components for functional data

JOURNAL OF MULTIVARIATE ANALYSIS

卷:133

Article

Bali, Juan Lucas¹  Boente, Graciela¹ 

[1] Univ Buenos Aires, Fac Ciencias Exactas & Nat, RA-1053 Buenos Aires, DF, Argentina

关键词: Elliptical distribution;    Fisher-consistency;    Functional principal component;    Influence function;    Robust estimation;    Smoothing;   

DOI  :  10.1016/j.jmva.2014.09.004

来源: Elsevier

【 摘 要 】

In the finite-dimensional setting, Li and Chen (1985) proposed a method for principal components analysis using projection-pursuit techniques. This procedure was generalized to the functional setting by Bali et al. (2011), where also different penalized estimators were defined to provide smooth functional robust principal component estimators. This paper completes their study by deriving the influence function of the functional related to the principal direction estimators and their size. As is well known, the influence function is a measure of robustness which can also be used for diagnostic purposes. In this sense, the obtained results can be helpful for detecting influential observations for the principal directions. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free