Improved model selection method for a regression function with dependent noise. (English) Zbl 1122.62023

Summary: This paper is devoted to nonparametric estimation, through the \(\mathcal{L}_2\)-risk, of a regression function based on observations with spherically symmetric errors, which are dependent random variables (except in the normal case). We apply a model selection approach using improved estimates. In a nonasymptotic setting, an upper bound for the risk is obtained (oracle inequality). Moreover asymptotic properties are given, such as upper and lower bounds for the risk, which provide optimal rates of convergence for penalized estimators.


62G08 Nonparametric regression and quantile regression
62H12 Estimation in multivariate analysis
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