Regression in random design and wavelet block thresholding
Résumé
The problem of estimating an unknown regression function in a regression setting with (known) random design is concerned. By adopting the minimax point of view, we explore the asymptotic performances of an adaptive estimator based on wavelet block thresholding under the global Lp risk (p>1). We show that the estimator achieves the optimal rates of convergence over a wide range of Besov balls.