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Article Dans Une Revue Annales de l'ISUP Année : 2019

Efficient prediction in L2-differentiable families of distributions

Emmanuel Onzon
  • Fonction : Auteur

Résumé

A proof of the Cramér-Rao inequality for prediction is presented under conditions of L2-differentiability of the family of distributions of the model. The assumptions and the proof differ from those of Miyata (2001) who also proved this inequality under L2-differentiability conditions. It is also proved that if an efficient predictor (i.e. which risk attains the bound) exists then the family of distributions is of a special form which can be seen as an extension of the notion of exponential family. This result is also proved under L2-differentiability conditions.
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Dates et versions

hal-03604355 , version 1 (10-03-2022)

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Emmanuel Onzon. Efficient prediction in L2-differentiable families of distributions. Annales de l'ISUP, 2019, 63 (2-3), pp.33-44. ⟨hal-03604355⟩

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