Unbiased risk estimation method for covariance estimation
ESAIM: Probability and Statistics, Volume 18 (2014), p. 251-264
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We consider a model selection estimator of the covariance of a random process. Using the Unbiased Risk Estimation (U.R.E.) method, we build an estimator of the risk which allows to select an estimator in a collection of models. Then, we present an oracle inequality which ensures that the risk of the selected estimator is close to the risk of the oracle. Simulations show the efficiency of this methodology.

DOI : https://doi.org/10.1051/ps/2013034
Classification:  62G05
Keywords: covariance estimation, model selection, U.R.E. method
@article{PS_2014__18__251_0,
     author = {Lescornel, H\'el\`ene and Loubes, Jean-Michel and Chabriac, Claudie},
     title = {Unbiased risk estimation method for covariance estimation},
     journal = {ESAIM: Probability and Statistics},
     publisher = {EDP-Sciences},
     volume = {18},
     year = {2014},
     pages = {251-264},
     doi = {10.1051/ps/2013034},
     language = {en},
     url = {http://www.numdam.org/item/PS_2014__18__251_0}
}
Lescornel, Hélène; Loubes, Jean-Michel; Chabriac, Claudie. Unbiased risk estimation method for covariance estimation. ESAIM: Probability and Statistics, Volume 18 (2014) pp. 251-264. doi : 10.1051/ps/2013034. http://www.numdam.org/item/PS_2014__18__251_0/

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