On the concept of depth for functional data

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dc.contributor.author López Pintado, Sara
dc.contributor.author Romo, Juan
dc.date.accessioned 2006-11-09T10:59:41Z
dc.date.available 2006-11-09T10:59:41Z
dc.date.issued 2006-05
dc.identifier.uri http://hdl.handle.net/10016/243
dc.description.abstract The statistical analysis of functional data is a growing need in many research areas. We propose a new depth notion for functional observations based on the graphic representation of the curves. Given a collection of functions, it allows to establish the centrality of a function and provides a natural center-outward ordering of the sample curves. Robust statistics such as the median function or a trimmed mean function can be defined from this depth definition. Its finite-dimensional version provides a new depth for multivariate data that is computationally very fast and turns out to be convenient to study high-dimensional observations. The natural properties are established for the new depth and the uniform consistency of the sample depth is proved. Simulation results show that the trimmed mean presents a better behavior than the mean for contaminated models. Several real data sets are considered to illustrate this new concept of depth. Finally, we use this new depth to generalize to functions the Wilcoxon rank sum test. It allows to decide whether two groups of curves come from the same population. This functional rank test is applied to girls and boys growth curves concluding that they present different growth patterns.
dc.format.extent 940225 bytes
dc.format.mimetype application/pdf
dc.language.iso eng
dc.language.iso eng
dc.relation.ispartofseries UC3M Working Papers. Statistics and Econometrics
dc.relation.ispartofseries 2006-12
dc.title On the concept of depth for functional data
dc.type workingPaper
dc.subject.eciencia Estadística
dc.rights.accessRights openAccess
dc.identifier.repec ws063012
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