ENBIS-13 in Ankara

15 – 19 September 2013 Abstract submission: 5 February – 5 June 2013

Strategies for Outlier Detection in Linear Regression with Functional Response

16 September 2013, 15:25 – 15:45

Abstract

Submitted by
André Rehage
Authors
André Rehage (TU Dortmund University), Sonja Kuhnt (TU Dortmund University)
Abstract
Functional data analysis is a branch of statistics capturing the specific properties of data which are continuously observed over a certain interval and therefore assumed to be smooth [1]. For instance, functional data occur in meteorology (like temperature over time) or psychometrics (like the ability space curve); moreover the functional aspect is intrinsic in most industrial processes. Recently, statistical methods like principal component analysis or generalized linear models [2] have been extended to functional data. We focus on generalized linear models with functional response and scalar covariates. As in every data analysis also in the analysis of functional data outliers, hence unusual observations can occur. We use the concept of data depth which has been extended to functional data [3] as well as an own approach to define outlier detection methods in the functional case.

Our work is motivated by an application to a thermal spraying process. Here, particle properties in flight are measured during the whole spraying process, which can be influenced by a number of process parameters. The particle properties can be assumed to be functional response variables in a generalized linear model of the spraying process. This real life example will be scanned for location and shape outliers.

References:

[1] Ramsay, J.O. and Silverman, B.W. (2005): Functional Data Analysis, 2nd edition, Springer, New York.
[2] Müller, H.-G. and Stadtmüller U. (2005): Generalized Functional Linear Models, Ann. Stat., 33(2), 774-805.
[3] López-Pintado, S. and Romo, J. (2009): On the Concept of Depth for Functional Data, JASA, 104(486), 718-734.

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