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Ein äquivarianter Schätzer ist ein spezieller Punktschätzer in der Schätztheorie, einem Teilgebiet der mathematischen Statistik. Äquivariante Schätzer zeichnen sich im einfachsten Fall dadurch aus, dass eine Transformation der Daten zu einer identischen Transformation des Schätzwertes führt. Verschiebt man die Daten also um einen gewissen Wert, so ist der Schätzwert ebenso um diesen Wert verschoben. Für äquivariante Schätzer lassen sich einige Optimalitätsbedingungen leichter zeigen. So sind beispielsweise unter gewissen Zusatzannahmen lokal minimale äquivariante Schätzer immer auch gleichmäßig beste erwartungstreue Schätzer. Wichtige äquivariante Schätzer sind die . (de) In statistics, the concept of being an invariant estimator is a criterion that can be used to compare the properties of different estimators for the same quantity. It is a way of formalising the idea that an estimator should have certain intuitively appealing qualities. Strictly speaking, "invariant" would mean that the estimates themselves are unchanged when both the measurements and the parameters are transformed in a compatible way, but the meaning has been extended to allow the estimates to change in appropriate ways with such transformations. The term equivariant estimator is used in formal mathematical contexts that include a precise description of the relation of the way the estimator changes in response to changes to the dataset and parameterisation: this corresponds to the use of "equivariance" in more general mathematics. (en) |
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Ein äquivarianter Schätzer ist ein spezieller Punktschätzer in der Schätztheorie, einem Teilgebiet der mathematischen Statistik. Äquivariante Schätzer zeichnen sich im einfachsten Fall dadurch aus, dass eine Transformation der Daten zu einer identischen Transformation des Schätzwertes führt. Verschiebt man die Daten also um einen gewissen Wert, so ist der Schätzwert ebenso um diesen Wert verschoben. (de) In statistics, the concept of being an invariant estimator is a criterion that can be used to compare the properties of different estimators for the same quantity. It is a way of formalising the idea that an estimator should have certain intuitively appealing qualities. Strictly speaking, "invariant" would mean that the estimates themselves are unchanged when both the measurements and the parameters are transformed in a compatible way, but the meaning has been extended to allow the estimates to change in appropriate ways with such transformations. The term equivariant estimator is used in formal mathematical contexts that include a precise description of the relation of the way the estimator changes in response to changes to the dataset and parameterisation: this corresponds to the use of (en) |
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Äquivarianter Schätzer (de) Invariant estimator (en) |
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