Mixing Least-Squares Estimators when the Variance is Unknown

Details Mixing Least-Squares Estimators when the Variance is Unknown Mixing Least-Squares Estimators when the Variance is Unknown

2007-11-02

arxiv.org/abs/0711.0372v1

Mathematics

Statistics Theory

30 pages

Scientific paper

We propose a procedure to handle the problem of Gaussian regression when the variance is unknown. We mix least-squares estimators from various models according to a procedure inspired by that of Leung and Barron (2007). We show that in some cases the resulting estimator is a simple shrinkage estimator. We then apply this procedure in various statistical settings such as linear regression or adaptive estimation in Besov spaces. Our results provide non-asymptotic risk bounds for the Euclidean risk of the estimator.

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