Detección de puntos de cambio en la función de media para datos funcionales multivariados
gráficas, ilustraciones, tablas
- Autores:
-
Latorre Montoya, Darío Alejandro
- Tipo de recurso:
- Fecha de publicación:
- 2021
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/80585
- Palabra clave:
- 510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas
510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas
Datos funcionales multivariados
Punto de cambio
Análisis de componentes principales
RKHS
Detection change point
Multivariate Functional Data
Change point
Principal Component Analysis
Hilbert spaces
- Rights
- openAccess
- License
- Reconocimiento 4.0 Internacional
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| dc.title.spa.fl_str_mv |
Detección de puntos de cambio en la función de media para datos funcionales multivariados |
| dc.title.translated.eng.fl_str_mv |
Detection changes points in the mean function for multivariate functional data |
| title |
Detección de puntos de cambio en la función de media para datos funcionales multivariados |
| spellingShingle |
Detección de puntos de cambio en la función de media para datos funcionales multivariados 510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas 510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas Datos funcionales multivariados Punto de cambio Análisis de componentes principales RKHS Detection change point Multivariate Functional Data Change point Principal Component Analysis Hilbert spaces |
| title_short |
Detección de puntos de cambio en la función de media para datos funcionales multivariados |
| title_full |
Detección de puntos de cambio en la función de media para datos funcionales multivariados |
| title_fullStr |
Detección de puntos de cambio en la función de media para datos funcionales multivariados |
| title_full_unstemmed |
Detección de puntos de cambio en la función de media para datos funcionales multivariados |
| title_sort |
Detección de puntos de cambio en la función de media para datos funcionales multivariados |
| dc.creator.fl_str_mv |
Latorre Montoya, Darío Alejandro |
| dc.contributor.advisor.none.fl_str_mv |
Guevara González, Rubén Darío |
| dc.contributor.author.none.fl_str_mv |
Latorre Montoya, Darío Alejandro |
| dc.subject.ddc.spa.fl_str_mv |
510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas 510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas |
| topic |
510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas 510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas Datos funcionales multivariados Punto de cambio Análisis de componentes principales RKHS Detection change point Multivariate Functional Data Change point Principal Component Analysis Hilbert spaces |
| dc.subject.proposal.spa.fl_str_mv |
Datos funcionales multivariados Punto de cambio Análisis de componentes principales |
| dc.subject.proposal.eng.fl_str_mv |
RKHS Detection change point Multivariate Functional Data Change point Principal Component Analysis Hilbert spaces |
| description |
gráficas, ilustraciones, tablas |
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2021 |
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2021-10-20T15:26:41Z |
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2021-10-20T15:26:41Z |
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2021-07 |
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Trabajo de grado - Maestría |
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info:eu-repo/semantics/masterThesis |
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http://purl.org/redcol/resource_type/TM |
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https://repositorio.unal.edu.co/handle/unal/80585 |
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Universidad Nacional de Colombia |
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Repositorio Institucional Universidad Nacional de Colombia |
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https://repositorio.unal.edu.co/ |
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https://repositorio.unal.edu.co/handle/unal/80585 https://repositorio.unal.edu.co/ |
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spa |
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Anderson, T. (2003). An Introduction to Multivariate Statistical Analysis. Wiley Series in Probability and Statistics. Arlot, S., Celisse, A., and Harchaoui, Z. (2019). A kernel multiple change-point algorithm via model selection. Journal of Machine Learning Research, 20(162):1–56. Aston, J. A. and Kirch, C. (2011). Estimation of the distribution of change-points with application to fmri data. Bardsley, P., Horváth, L., Kokoszka, P., and Young, G. (2017). Change point tests in functional factor models with application to yield curves. The Econometrics Journal, 20(1):86–117. Berkes, I., Gabrys, R., Horv´ath, L., and Kokoszka, P. (2009). Detecting changes in the mean of functional observations. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 71(5):927–946. Berrendero, J. R., Bueno-Larraz, B., and Cuevas, A. (2020). On mahalanobis distance in functional settings. Journal of Machine Learning Research, 21(9):1–33. Berrendero, J. 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). Multivariate functional principal component analysis for data observed on different (dimensional) domains. Journal of the American Statistical Association, 113(522):649–659. Happ-Kurz, C. (2020). Object-oriented software for functional data. Journal of Statistical Software, 93(5):1–38. Hawkins, D. M., Qiu, P., and Kang, C. W. (2003). The changepoint model for statistical process control. Journal of quality technology, 35(4):355–366. Helwig, N., Pignanelli, E., and Schütze, A. (2015). Condition monitoring of a complex hydraulic system using multivariate statistics. In 2015 IEEE International Instrumentation and Measurement Technology Conference (I2MTC) Proceedings, pages 210–215. IEEE. Hormann, S., Kidzinski, L., and Hallin, M. (2015). Dynamic functional principal components. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 77(2):319–348. Horváth, L. and Kokoszka, P. (2012). Inference for functional data with applications, volume 200. 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. Journal of Statistical Theory and Practice, 4(4):643–662. Page, E. (1955). A test for a change in a parameter occurring at an unknown point. Biometrika, 42(3/4):523–527. Page, E. S. (1954). Continuous inspection schemes. Biometrika, 41(1/2):100–115. Plummer, P. J. and Chen, J. (2014). A bayesian approach for locating change points in a compound poisson process with application to detecting dna copy number variations. Journal of Applied Statistics, 41(2):423–438. Ramsay, J. O. (2004). Functional data analysis. Encyclopedia of Statistical Sciences, 4. Saitoh, S. and Sawano, Y. (2016). Theory of reproducing kernels and applications. Springer. Sen, A. K. and Srivastava, M. S. (1973). On multivariate tests for detecting change in mean. Sankhy¯a: The Indian Journal of Statistics, Series A, pages 173–186. Sharipov, O., Tewes, J., and Wendler, M. (2016). Sequential block bootstrap in a hilbert space with application to change point analysis. Canadian Journal of Statistics, 44(3):300–322. 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. |
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Departamento de Estadística |
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Facultad de Ciencias |
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Bogotá, Colombia |
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Universidad Nacional de Colombia - Sede Bogotá |
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Reconocimiento 4.0 Internacionalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Guevara González, Rubén Darío1576c12a39d4ac35f1f710837eff755bLatorre Montoya, Darío Alejandroe880ec1f9c77e5ce7c7e4ddd03b2317a2021-10-20T15:26:41Z2021-10-20T15:26:41Z2021-07https://repositorio.unal.edu.co/handle/unal/80585Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/gráficas, ilustraciones, tablasEl 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)The 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.MaestríaMagíster en Ciencias - EstadísticaAnálisis de datos funcionalesxiv, 98 páginasapplication/pdfspa510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas510 - Matemáticas::519 - Probabilidades y matemáticas aplicadasDatos funcionales multivariadosPunto de cambioAnálisis de componentes principalesRKHSDetection change pointMultivariate Functional DataChange pointPrincipal Component AnalysisHilbert spacesDetección de puntos de cambio en la función de media para datos funcionales multivariadosDetection changes points in the mean function for multivariate functional dataTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMBogotá - Ciencias - Maestría en Ciencias - EstadísticaDepartamento de EstadísticaFacultad de CienciasBogotá, ColombiaUniversidad Nacional de Colombia - Sede BogotáAnderson, T. (2003). An Introduction to Multivariate Statistical Analysis. Wiley Series in Probability and Statistics. Arlot, S., Celisse, A., and Harchaoui, Z. (2019). A kernel multiple change-point algorithm via model selection. Journal of Machine Learning Research, 20(162):1–56. Aston, J. A. and Kirch, C. (2011). Estimation of the distribution of change-points with application to fmri data. Bardsley, P., Horváth, L., Kokoszka, P., and Young, G. (2017). Change point tests in functional factor models with application to yield curves. The Econometrics Journal, 20(1):86–117. Berkes, I., Gabrys, R., Horv´ath, L., and Kokoszka, P. (2009). Detecting changes in the mean of functional observations. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 71(5):927–946. Berrendero, J. R., Bueno-Larraz, B., and Cuevas, A. (2020). On mahalanobis distance in functional settings. Journal of Machine Learning Research, 21(9):1–33. Berrendero, J. 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). Multivariate functional principal component analysis for data observed on different (dimensional) domains. Journal of the American Statistical Association, 113(522):649–659. Happ-Kurz, C. (2020). Object-oriented software for functional data. Journal of Statistical Software, 93(5):1–38. Hawkins, D. M., Qiu, P., and Kang, C. W. (2003). The changepoint model for statistical process control. Journal of quality technology, 35(4):355–366. Helwig, N., Pignanelli, E., and Schütze, A. (2015). Condition monitoring of a complex hydraulic system using multivariate statistics. In 2015 IEEE International Instrumentation and Measurement Technology Conference (I2MTC) Proceedings, pages 210–215. IEEE. Hormann, S., Kidzinski, L., and Hallin, M. (2015). Dynamic functional principal components. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 77(2):319–348. Horváth, L. and Kokoszka, P. (2012). Inference for functional data with applications, volume 200. 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. Journal of Statistical Theory and Practice, 4(4):643–662. Page, E. (1955). A test for a change in a parameter occurring at an unknown point. Biometrika, 42(3/4):523–527. Page, E. S. (1954). Continuous inspection schemes. Biometrika, 41(1/2):100–115. Plummer, P. J. and Chen, J. (2014). A bayesian approach for locating change points in a compound poisson process with application to detecting dna copy number variations. Journal of Applied Statistics, 41(2):423–438. Ramsay, J. O. (2004). Functional data analysis. Encyclopedia of Statistical Sciences, 4. Saitoh, S. and Sawano, Y. (2016). Theory of reproducing kernels and applications. Springer. Sen, A. K. and Srivastava, M. S. (1973). On multivariate tests for detecting change in mean. Sankhy¯a: The Indian Journal of Statistics, Series A, pages 173–186. Sharipov, O., Tewes, J., and Wendler, M. (2016). Sequential block bootstrap in a hilbert space with application to change point analysis. Canadian Journal of Statistics, 44(3):300–322. 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.Público generalORIGINAL1013597149_2021.pdf1013597149_2021.pdfTesis de Maestría en Estadísticaapplication/pdf2437410https://repositorio.unal.edu.co/bitstream/unal/80585/2/1013597149_2021.pdf826339d772b0c824dd76f76daaa5f648MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-83964https://repositorio.unal.edu.co/bitstream/unal/80585/6/license.txtcccfe52f796b7c63423298c2d3365fc6MD56THUMBNAIL1013597149_2021.pdf.jpg1013597149_2021.pdf.jpgGenerated Thumbnailimage/jpeg4387https://repositorio.unal.edu.co/bitstream/unal/80585/7/1013597149_2021.pdf.jpg9e1f5c3e69ae2c64bd54fc3e51a8c927MD57unal/80585oai:repositorio.unal.edu.co:unal/805852024-07-30 23:11:20.7Repositorio Institucional Universidad Nacional de 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