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.
Mots clés : 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},
pages = {251--264},
publisher = {EDP-Sciences},
volume = {18},
year = {2014},
doi = {10.1051/ps/2013034},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ps/2013034/}
}
TY - JOUR AU - Lescornel, Hélène AU - Loubes, Jean-Michel AU - Chabriac, Claudie TI - Unbiased risk estimation method for covariance estimation JO - ESAIM: Probability and Statistics PY - 2014 SP - 251 EP - 264 VL - 18 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ps/2013034/ DO - 10.1051/ps/2013034 LA - en ID - PS_2014__18__251_0 ER -
%0 Journal Article %A Lescornel, Hélène %A Loubes, Jean-Michel %A Chabriac, Claudie %T Unbiased risk estimation method for covariance estimation %J ESAIM: Probability and Statistics %D 2014 %P 251-264 %V 18 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ps/2013034/ %R 10.1051/ps/2013034 %G en %F PS_2014__18__251_0
Lescornel, Hélène; Loubes, Jean-Michel; Chabriac, Claudie. Unbiased risk estimation method for covariance estimation. ESAIM: Probability and Statistics, Tome 18 (2014), pp. 251-264. doi : 10.1051/ps/2013034. http://archive.numdam.org/articles/10.1051/ps/2013034/
[1] , An introduction to continuity, extrema, and related topics for general gaussian processes. Lect. Note Ser. Institute of Mathematical Statistics (1990). | MR | Zbl
[2] and , Covariance regularization by thresholding. Ann. Statist. 36 (2008) 2577-2604. | MR | Zbl
[3] , , and , Group lasso estimation of high-dimensional covariance matrices. J. Machine Learn. Res. (2011). | MR | Zbl
[4] , , and , Nonparametric estimation of covariance functions by model selection. Electron. J. Statis. 4 (2010) 822-855. | MR
[5] , , and , Adaptive estimation of spectral densities via wavelet thresholding and information projection (2010).
[6] , and , Cross-validation of covariance structures using the frobenius matrix distance as a discrepancy function. J. Stat. Comput. Simul. 58 (1997) 195-215. | Zbl
[7] and , Nonparametric covariance function estimation for functional and longitudinal data. Technical report (2010).
[8] , Statistics for spatial data. Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics. Revised reprint of the 1991 edition, A Wiley-Interscience Publication. John Wiley and Sons Inc., New York (1993). | MR | Zbl
[9] and , Nonparametric estimation of covariance structure in longitudinal data. Biometrics 54 (1998) 401-415. | Zbl
[10] , Kriging in terms of projections. J. Int. Assoc. Math. Geol. 9 (1977) 563-586. | MR
[11] , Linear statistical inference and its applications. Wiley ser. Probab. Stastis. Wiley, 2nd edn. (1973). | MR | Zbl
[12] , A matrix handbook for statisticians. Wiley ser. Probab. Stastis. Wiley (2008). | MR | Zbl
[13] and , Empirical processes with applications to statistics. Wiley (1986). | MR | Zbl
[14] , Estimation of the mean of a multivariate normal distribution. Ann. Statis. 9 (1981) 1135-1151. | MR | Zbl
[15] . Interpolation of spatial data. Some theory for Kriging. Springer Ser. Statis. Springer-Verlag, New York (1999). | MR | Zbl
[16] , Introduction à l'estimation non-paramétrique. Vol. 41 of Math. Appl. Springer (2004). | MR | Zbl
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