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The James–Stein estimator is a biased estimator of the mean, , of (possibly) correlated Gaussian distributed random vectors with unknown means . It arose sequentially in two main published papers, the earlier version of the estimator was developed by Charles Stein in 1956, which reached a relatively shocking conclusion that while the then usual estimate of the mean, or the sample mean written by Stein and James as , is admissible when , however it is inadmissible when and proposed a possible improvement to the estimator that shrinks the sample means towards a more central mean vector (which can be chosen a priori or commonly the "average of averages" of the sample means given all samples share the same size), is commonly referred to as Stein's example or paradox. This earlier result wa

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  • James-Stein-Schätzer sind Schätzfunktionen des Erwartungswertvektors einer mehrdimensionalen Normalverteilung. Wenn diese Normalverteilung mindestens dreidimensional ist, sind James-Stein-Schätzer bzgl. des mittleren quadratischen Fehlers gleichmäßig besser als das üblicherweise als Schätzer benutzte arithmetische Mittel. Das arithmetische Mittel ist also im Sinne der Entscheidungstheorie für Dimensionen größer als zwei keine zulässige Entscheidungsfunktion für den Erwartungswertvektor der Normalverteilung. Diese Tatsache wurde 1956 von Charles Stein entdeckt. Der erste James-Stein-Schätzer geht auf eine Arbeit von W. James und C. Stein aus dem Jahre 1961 zurück. (de)
  • The James–Stein estimator is a biased estimator of the mean, , of (possibly) correlated Gaussian distributed random vectors with unknown means . It arose sequentially in two main published papers, the earlier version of the estimator was developed by Charles Stein in 1956, which reached a relatively shocking conclusion that while the then usual estimate of the mean, or the sample mean written by Stein and James as , is admissible when , however it is inadmissible when and proposed a possible improvement to the estimator that shrinks the sample means towards a more central mean vector (which can be chosen a priori or commonly the "average of averages" of the sample means given all samples share the same size), is commonly referred to as Stein's example or paradox. This earlier result was improved later by Willard James and Charles Stein in 1961 through simplifying the original process. It can be shown that the James–Stein estimator dominates the "ordinary" least squares approach, meaning the James–Stein estimator has a lower or equal mean squared error than the "ordinary" least square estimator. (en)
  • El estimador de James-Stein es un estimador sesgado de la media de los vectores aleatorios gaussianos. Se puede demostrar que el estimador de James-Stein domina el enfoque de los mínimos cuadrados, es decir, tiene un error cuadrático medio menor. Es el ejemplo más conocido del . Una versión anterior del estimador fue desarrollado por Charles Stein en 1956,​ y se refiere a veces como estimador de Stein. El resultado fue mejorado por Willard James y Charles Stein en 1961.​ (es)
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  • James-Stein-Schätzer sind Schätzfunktionen des Erwartungswertvektors einer mehrdimensionalen Normalverteilung. Wenn diese Normalverteilung mindestens dreidimensional ist, sind James-Stein-Schätzer bzgl. des mittleren quadratischen Fehlers gleichmäßig besser als das üblicherweise als Schätzer benutzte arithmetische Mittel. Das arithmetische Mittel ist also im Sinne der Entscheidungstheorie für Dimensionen größer als zwei keine zulässige Entscheidungsfunktion für den Erwartungswertvektor der Normalverteilung. Diese Tatsache wurde 1956 von Charles Stein entdeckt. Der erste James-Stein-Schätzer geht auf eine Arbeit von W. James und C. Stein aus dem Jahre 1961 zurück. (de)
  • El estimador de James-Stein es un estimador sesgado de la media de los vectores aleatorios gaussianos. Se puede demostrar que el estimador de James-Stein domina el enfoque de los mínimos cuadrados, es decir, tiene un error cuadrático medio menor. Es el ejemplo más conocido del . Una versión anterior del estimador fue desarrollado por Charles Stein en 1956,​ y se refiere a veces como estimador de Stein. El resultado fue mejorado por Willard James y Charles Stein en 1961.​ (es)
  • The James–Stein estimator is a biased estimator of the mean, , of (possibly) correlated Gaussian distributed random vectors with unknown means . It arose sequentially in two main published papers, the earlier version of the estimator was developed by Charles Stein in 1956, which reached a relatively shocking conclusion that while the then usual estimate of the mean, or the sample mean written by Stein and James as , is admissible when , however it is inadmissible when and proposed a possible improvement to the estimator that shrinks the sample means towards a more central mean vector (which can be chosen a priori or commonly the "average of averages" of the sample means given all samples share the same size), is commonly referred to as Stein's example or paradox. This earlier result wa (en)
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  • James-Stein-Schätzer (de)
  • Estimador de James-Stein (es)
  • James–Stein estimator (en)
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