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http://cimat.repositorioinstitucional.mx/jspui/handle/1008/1082| ROBUST ESTIMATION OF THE MEAN OF A RANDOM MATRIX: A NONASYMPTOTIC STUDY | |
| Roberto Cabal | |
| Acceso Abierto | |
| Atribución-NoComercial | |
| PROBABILIDAD Y ESTADÍSTICA | |
| This thesis is concerned with the estimation of the mean of a random matrix when there are no assumptions about the tail of the distributions that are related to the matrix. More specifically, the estimation procedure contemplates that the distribution of the elements of the random matrix could be heavy-tailed. For this reason, we develop concentration inequalities for the estimators around the mean matrix in such a way that the theoretical guarantees give us, for example, valuable information about how to choose the hyperparameters related to the estimator. Of particular interest is the robust estimation of the covariance matrix from a random sample, which has numerous applications in statistical science such as Factor Analysis and Principal Components Analysis. Other famous applications of matrix concentration inequalities are in the fields of Matrix Completion and community detection in Random Graphs Theory. | |
| 30-10-2020 | |
| Tesis de maestría | |
| OTRAS | |
| Versión aceptada | |
| acceptedVersion - Versión aceptada | |
| Aparece en las colecciones: | Tesis del CIMAT |
Cargar archivos:
| Fichero | Descripción | Tamaño | Formato | |
|---|---|---|---|---|
| TE 785.pdf | 3.17 MB | Adobe PDF | Visualizar/Abrir |