arXiv subjects

Emmanuel Onzon

Publications and source records attributed to Emmanuel Onzon.

2 recordsLinked to original sources

arXiv2014

Efficient prediction in $L^2$-differentiable families of distributions

A proof of the Cramér-Rao inequality for prediction is presented under conditions of $L^2$-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 $L^2$-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 $L^2$-differentiability conditions.

math.ST↗

arXiv2013

Asymptotically efficient prediction for LAN families

In a previous paper (Bosq & Onzon (2012)) we did a first generalization of the concept of asymptotic efficiency for statistical prediction, i.e. for the problems where the unknown quantity to infer is not deterministic but random. However, in some instances, the assumptions we made were not easy to verify. Here we give proofs of similar results based on quite a different set of assumptions. The model is required to be a LAN family, which allows to use the convolution theorem of Hájek and Le Cam. The results are applied to the forecasting of a bivariate Ornstein-Uhlenbeck process, for which the assumptions of Bosq & Onzon (2012) are tricky to verify.

math.ST↗