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Adaptive estimation in regression and complexity of approximation of random fields
regression and complexity approximation random fields
2012/9/17
In this thesis we study adaptive nonparametric regression with noise misspecifi-cation and the complexity of approximation of random fields in dependence of the dimension.
First, we consider the prob...
Adaptive estimation of covariance matrices via Cholesky decomposition
Covariance matrix banding Cholesky decomposition
2010/10/19
This paper studies the estimation of a large covariance matrix. We introduce a novel procedure called ChoSelect based on the Cholesky factor of the inverse covariance. This method uses a dimension red...
Adaptive estimation of linear functionals by model selection
Nonparametric regression white noise model adaptive estimation model selection pointwise adaptive estimation
2009/9/16
We propose an estimation procedure for linear functionals based on Gaussian model selection techniques. We show that the procedure is adaptive, and we give a non asymptotic oracle inequality for the r...