Statistical learning methods for functional data with applications to prediction, classification and outlier detection

Hernández Banadik, Nicolás Jorge

Publication:
Statistical learning methods for functional data with applications to prediction, classification and outlier detection

dc.contributor.advisor	Muñoz García, Alberto
dc.contributor.author	Hernández Banadik, Nicolás Jorge
dc.contributor.departamento	UC3M. Departamento de Estadística	es
dc.contributor.funder	Ministerio de Economía y Competitividad (España)	es
dc.date.accessioned	2019-12-11T19:26:36Z
dc.date.available	2019-12-11T19:26:36Z
dc.date.issued	2019-07
dc.date.submitted	2019-07-18
dc.description.abstract	In the era of big data, Functional Data Analysis has become increasingly important insofar as it constitutes a powerful tool to tackle inference problems in statistics. In particular in this thesis we have proposed several methods aimed to solve problems of prediction of time series, classification and outlier detection from a functional approach. The thesis is organized as follows: In Chapter 1 we introduce the concept of functional data and state the overview of the thesis. In Chapter 2 of this work we present the theoretical framework used to we develop the proposed methodologies. In Chapters 3 and 4 two new ordering mappings for functional data are proposed. The first is a Kernel depth measure, which satisfies the corresponding theoretical properties, while the second is an entropy measure. In both cases we propose a parametric and non-parametric estimation method that allow us to define an order in the data set at hand. A natural application of these measures is the identification of atypical observations (functions). In Chapter 5 we study the Functional Autoregressive Hilbertian model. We also propose a new family of basis functions for the estimation and prediction of the aforementioned model, which belong to a reproducing kernel Hilbert space. The properties of continuity obtained in this space allow us to construct confidence bands for the corresponding predictions in a detracted time horizon. In order to boost different classification methods, in Chapter 6 we propose a divergence measure for functional data. This metric allows us to determine in which part of the domain two classes of functional present divergent behavior. This methodology is framed in the field of domain selection, and it is aimed to solve classification problems by means of the elimination of redundant information. Finally in Chapter 7 the general conclusions of this work and the future research lines are presented.	en
dc.description.degree	Programa de Doctorado en Economía de la Empresa y Métodos Cuantitativos por la Universidad Carlos III de Madrid	es
dc.description.responsability	Presidente: Santiago Velilla Cerdán; Secretario: Kalliopi Mylona; Vocal: Luis Antonio Belanche Muñoz	es
dc.description.sponsorship	Financial support received from the Spanish Ministry of Economy and Competitiveness ECO2015-66593-P and the UC3M PIF scholarship for doctoral studies.	en
dc.identifier.uri	https://hdl.handle.net/10016/29347
dc.language.iso	eng	es
dc.relation.projectID	Gobierno de España. ECO2015-66593-P	es
dc.rights	Atribución-NoComercial-SinDerivadas 3.0 España	*
dc.rights.accessRights	open access	es
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/3.0/es/	*
dc.subject.eciencia	Estadística	es
dc.subject.other	Estadística	es
dc.subject.other	Análisis de datos	es
dc.title	Statistical learning methods for functional data with applications to prediction, classification and outlier detection	en
dc.type	doctoral thesis	*
dspace.entity.type	Publication