RT Dissertation/Thesis
T1 Statistical learning methods for functional data with applications to prediction, classification and outlier detection
A1 Hernández Banadik, Nicolás Jorge
AB In the era of big data, Functional Data Analysis has become increasingly important insofaras it constitutes a powerful tool to tackle inference problems in statistics. In particularin this thesis we have proposed several methods aimed to solve problems ofprediction 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 functionaldata and state the overview of the thesis. In Chapter 2 of this work we presentthe 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 parametricand non-parametric estimation method that allow us to define an order in the data setat 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 alsopropose a new family of basis functions for the estimation and prediction of the aforementionedmodel, which belong to a reproducing kernel Hilbert space. The propertiesof continuity obtained in this space allow us to construct confidence bands for the correspondingpredictions in a detracted time horizon.In order to boost different classification methods, in Chapter 6 we propose a divergencemeasure for functional data. This metric allows us to determine in which part ofthe domain two classes of functional present divergent behavior. This methodology isframed in the field of domain selection, and it is aimed to solve classification problemsby means of the elimination of redundant information.Finally in Chapter 7 the general conclusions of this work and the future researchlines are presented.
YR 2019
FD 2019-07
LK https://hdl.handle.net/10016/29347
UL https://hdl.handle.net/10016/29347
LA eng
NO Financial support received from the Spanish Ministry of Economy and Competitiveness ECO2015-66593-P and the UC3M PIF scholarship for doctoral studies.
DS e-Archivo
RD 18 jul. 2024