Summary
If we are interested in making inferences about the square norm of the mean in a multivariate normal model, the usual uniform prior for the mean is not sound, as revealed by Stein in his 1959 work.
This paper studies in what sense this prior must be modified by using the maximization of missing information procedure (Bernardo, 1979).
Resumen
Stein (1959), en su artículo sobre la gran discrepancia entre intervalos de confianza e intervalos fiduciales, puso de relieve el comportamiento poco convincente de la distribución inicial uniforme para el vector de medias de una normal multivariante si nuestro interés se centra en hacer inferencias sobre el cuadrado de su norma.
En este artículo, utilizando el método de maximización de la información desconocida (Bernardo, 1979), se estudia en qué sentido la distribución inicial del vector de medias debe ser “corregida” mediante la obtención de la distribución inicial mínimo-informativa para el cuadrado de su norma y se exponen los resultados a que dicha corrección conduce.
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Ferrándiz, J.R. Una solucion bayesiana a la Paradoja de Stein. Trabajos de Estadistica Y de Investigacion Operativa 33, 31–46 (1982). https://doi.org/10.1007/BF02888621
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DOI: https://doi.org/10.1007/BF02888621