Jorba i Monte, ÀngelCasanovas Pato, Clàudia2022-04-082022-04-082021-06-20https://hdl.handle.net/2445/184858Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2021, Director: Àngel Jorba i Monte[en] The (population) mean of a $p$-dimensional multivariate normal vector is plainly estimated by the empirical mean which, additionally, is minimax, ML, UMV and least squares BLUE. One would fancy it is also best as to risk. Nonetheless, Stein (1956) proved it is inadmissible for $p>2$, showing alternative, better candidates. This is Stein's paradox, origin of this memoir. We begin with a brief introduction to place Stein's result in its proper historical context. Then, after reviewing some basic Statistics concepts we present Stein's result, accompanied by illustrative simulations. Finally we survey several approaches to understanding the paradox.48 p.application/pdfspacc-by-nc-nd (c) Clàudia Casanovas Pato, 2021codi: GPL (c) Clàudia Casanovas Pato, 2021http://creativecommons.org/licenses/by-nc-nd/3.0/es/http://www.gnu.org/licenses/gpl-3.0.ca.htmlAnàlisi multivariableTreballs de fi de grauTeoria de l'estimacióEstadística matemàticaMultivariate analysisBachelor's thesesEstimation theoryMathematical statisticsinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess