Detección de puntos de cambio en la función de media para datos funcionales multivariados

dc.contributor.advisorGuevara González, Rubén Darío
dc.contributor.authorLatorre Montoya, Darío Alejandro
dc.date.accessioned2021-10-20T15:26:41Z
dc.date.available2021-10-20T15:26:41Z
dc.date.issued2021-07
dc.descriptiongráficas, ilustraciones, tablasspa
dc.description.abstractEl objetivo del análisis de punto de cambio es identificar si existen cambios o no en la distribución de un proceso estocástico, determinando el tiempo del cambio cuando haya ocurrido. Para datos funcionales univariados existen metodologías de detección de cambio en la media, sin embargo, no hay propuestas explícitas para el caso multivariado. Se propone una metodología para la detección de punto de cambio en la media de datos funcionales multivariados basada en un espacio de funciones RKHS que es construido. Se define un estadístico por medio de la norma inducida por el producto interno en el RKHS. Se muestra que el estadístico usado en el caso univariado se puede generalizar para éste enfoque. El estadístico definido tiene en cuenta la estructura de covarianza multivariada en el tiempo y la funcional univariada para los procesos. Cambios en la media de procesos multivariados simulados con varias estructuras de covarianza son detectados correctamente por la propuesta. Dos aplicaciones de la metodología propuesta, la primera a una casa domótica y la otra a una plataforma hidráulica, detectan correctamente el punto de cambio. La metodología es aplicada a contaminantes en el aire de Bogotá para detectar el inicio de las medidas de cuarentena de 2020. Se desarrollan dos apps, una para realizar simulaciones y una para uso de la propuesta. (Texto tomado de la fuente)spa
dc.description.abstractThe change point analysis aims to identify whether or not there are changes in the stochastic process distribution, providing an estimate of the change time as required.There exist several methodologies to detect changes in the mean of univariate functional data, however, there are not explicit proposals in the multivariate case. We propose a methodology to detect the change point in the mean of Multivariate Functional Data based on a RKHS functions space that is constructed. We define a statistic using the RKHS inner product. We are able to show that a statistic used in the univariate case can be generalized from the perspective of our approach. The defined statistic takes into account a multivariate covariance structure at time as well as a univariate functional for the process.The changes in the mean on simulated multivariate processes for several covariance structures are detected properly using our proposal. We are able two applications of the proposed methodology, the first to a domotic house and the other to a hydraulic platform, correctly detect the point of change. The methodology is applied to air pollutants in Bogot´a to detect the start of 2020 quarantine measures. Two apps are developed, one to perform simulations and one to use the proposal.eng
dc.description.degreelevelMaestríaspa
dc.description.degreenameMagíster en Ciencias - Estadísticaspa
dc.description.researchareaAnálisis de datos funcionalesspa
dc.format.extentxiv, 98 páginasspa
dc.format.mimetypeapplication/pdfspa
dc.identifier.instnameUniversidad Nacional de Colombiaspa
dc.identifier.reponameRepositorio Institucional Universidad Nacional de Colombiaspa
dc.identifier.repourlhttps://repositorio.unal.edu.co/spa
dc.identifier.urihttps://repositorio.unal.edu.co/handle/unal/80585
dc.language.isospaspa
dc.publisher.branchUniversidad Nacional de Colombia - Sede Bogotáspa
dc.publisher.departmentDepartamento de Estadísticaspa
dc.publisher.facultyFacultad de Cienciasspa
dc.publisher.placeBogotá, Colombiaspa
dc.publisher.programBogotá - Ciencias - Maestría en Ciencias - Estadísticaspa
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R., Justel, A., and Svarc, M. (2011). Principal components for multivariate functional data. Computational Statistics & Data Analysis, 55(9):2619–2634. Chen, J. and Gupta, A. K. (2011). Parametric statistical change point analysis: with applications to genetics, medicine, and finance. Springer Science & Business Media. Chiou, J.-M., Chen, Y.-T., and Yang, Y.-F. (2014). Multivariate functional principal component analysis: A normalization approach. Statistica Sinica, pages 1571–1596. Dua, D. and Graff, C. (2017). UCI machine learning repository. Gardner, L. (1969). On detecting changes in the mean of normal variates. The Annals of Mathematical Statistics, 40(1):116–126. Garreau, D. (2017). Change-point detection and kernel methods. PhD thesis. Grines, V. Z., Medvedev, T. V., and Pochinka, O. V. (2016). Dynamical systems on 2-and 3-manifolds, volume 46. Springer. Hall, B. C. (2013). Lie Groups, Lie Algebras, and Representations. Springer. Happ, C. and Greven, S. (2018). 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Springer Science & Business Media. Hotelling, H. (1947). Multivariate quality control. techniques of statistical analysis. McGraw-Hill, New York. Hsing, T. and Eubank, R. (2015). Theoretical foundations of functional data analysis, with an introduction to linear operators. John Wiley & Sons. Huang, S., Kong, Z., and Huang, W. (2014). High-dimensional process monitoring and change point detection using embedding distributions in reproducing kernel hilbert space. IIE Transactions, 46(10):999–1016. Jacques, J. and Preda, C. (2014). Model-based clustering for multivariate functional data. Computational Statistics & Data Analysis, 71:92–106. Kiefer, J. (1959). K-sample analogues of the kolmogorov-smirnov and cram´er-v. mises tests. The Annals of Mathematical Statistics, pages 420–447. Latorre, D. (2019). Code change point for mfda thesis. https://github.com/ dalatorrem/code_tesis_PCMFD.git. Lee, T.-S. (2010). Change-point problems: bibliography and review. 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Skubalska-Rafaj lowicz, E. (2013). Random projections and hotelling’s t2 statistics for change detection in high-dimensional data streams. International Journal of Applied Mathematics and Computer Science, 23(2):447–461. Stoehr, C., Aston, J. A., and Kirch, C. (2020). Detecting changes in the covariance structure of functional time series with application to fmri data. Econometrics and Statistics. Vasudeva, H. L. and Shirali, S. (2017). Elements of Hilbert spaces and operator theory. Springer. Zamba, K. and Hawkins, D. M. (2009). A multivariate change-point model for change in mean vector and/or covariance structure. Journal of Quality Technology, 41(3):285–303. Zamora-Martinez, F., Romeu, P., Botella-Rocamora, P., and Pardo, J. (2014). On-line learning of indoor temperature forecasting models towards energy efficiency. Energy and Buildings, 83:162–172.spa
dc.rights.accessrightsinfo:eu-repo/semantics/openAccessspa
dc.rights.licenseReconocimiento 4.0 Internacionalspa
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/spa
dc.subject.ddc510 - Matemáticas::519 - Probabilidades y matemáticas aplicadasspa
dc.subject.ddc510 - Matemáticas::519 - Probabilidades y matemáticas aplicadasspa
dc.subject.proposalDatos funcionales multivariadosspa
dc.subject.proposalPunto de cambiospa
dc.subject.proposalAnálisis de componentes principalesspa
dc.subject.proposalRKHSeng
dc.subject.proposalDetection change pointeng
dc.subject.proposalMultivariate Functional Dataeng
dc.subject.proposalChange pointeng
dc.subject.proposalPrincipal Component Analysiseng
dc.subject.proposalHilbert spaceseng
dc.titleDetección de puntos de cambio en la función de media para datos funcionales multivariadosspa
dc.title.translatedDetection changes points in the mean function for multivariate functional dataeng
dc.typeTrabajo de grado - Maestríaspa
dc.type.coarhttp://purl.org/coar/resource_type/c_bdccspa
dc.type.coarversionhttp://purl.org/coar/version/c_ab4af688f83e57aaspa
dc.type.contentTextspa
dc.type.driverinfo:eu-repo/semantics/masterThesisspa
dc.type.redcolhttp://purl.org/redcol/resource_type/TMspa
dc.type.versioninfo:eu-repo/semantics/acceptedVersionspa
dcterms.audience.professionaldevelopmentPúblico generalspa
oaire.accessrightshttp://purl.org/coar/access_right/c_abf2spa

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