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The Mahalanobis distance for functional data with applications to classification

Esdras Joseph, Pedro Galeano and Rosa Elvira Lillo Rodríguez

DES - Working Papers. Statistics and Econometrics. WS from Universidad Carlos III de Madrid. Departamento de Estadística

Abstract: This paper presents a general notion of Mahalanobis distance for functional data that extends the classical multivariate concept to situations where the observed data are points belonging to curves generated by a stochastic process. More precisely, a new semi-distance for functional observations that generalize the usual Mahalanobis distance for multivariate datasets is introduced. For that, the development uses a regularized square root inverse operator in Hilbert spaces. Some of the main characteristics of the functional Mahalanobis semi-distance are shown. Afterwards, new versions of several well known functional classification procedures are developed using the Mahalanobis distance for functional data as a measure of proximity between functional observations. The performance of several well known functional classification procedures are compared with those methods used in conjunction with the Mahalanobis distance for functional data, with positive results, through a Monte Carlo study and the analysis of two real data examples

Keywords: Classification; methods; Functional; data; analysis; Functional; Mahalanobis; semi-distance; Functional; principal; components (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm
Date: 2013-05
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