ROBUST ESTIMATION OF THE MEAN OF A RANDOM MATRIX: A NONASYMPTOTIC STUDY
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 h...
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| Tipo de recurso: | tesis de maestría |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2020 |
| País: | México |
| Institución: | Centro de Investigación en Matemáticas |
| Repositorio: | Repositorio Institucional CIMAT |
| OAI Identifier: | oai:cimat.repositorioinstitucional.mx:1008/1082 |
| Acceso en línea: | http://cimat.repositorioinstitucional.mx/jspui/handle/1008/1082 |
| Access Level: | acceso abierto |
| Palabra clave: | info:eu-repo/classification/MSC/PROBABILIDAD Y ESTADÍSTICA info:eu-repo/classification/cti/1 info:eu-repo/classification/cti/12 info:eu-repo/classification/cti/1299 info:eu-repo/classification/cti/129999 |
| Sumario: | 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. |
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