Unbiased risk estimation method for covariance estimation

2011/12/20 by Hélène Lescornel, Lescornel, Hélène, Jean-Michel Loubes +3
Mathematics · #FOS: Mathematics #Statistics Theory (math.ST) #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1112.4735

arxiv created 2011/12/20 · arxiv updated 2011/12/22

Abstract

We consider a model selection estimator of the covariance of a random process. Using the Unbiased Risk Estimation (URE) method, we build an estimator of the risk which allows to select an estimator in a collection of model. 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.

Related

• Unbiased estimation of risk
• Nonparametric estimation of covariance functions by model selection
• Adaptive Covariance Estimation with model selection
• Optimal oracle inequalities for model selection
• Estimator selection with respect to Hellinger-type risks