A0485
Title: On optimal adaptive estimation of a density
Authors: Mathieu Sart - Universite Jean Monnet (France) [presenting]
Abstract: The problem of estimating a density $f$ is tackled on the real line $\mathbb{R}$. A new way of thresholding the coefficients in wavelet methods is presented. The risk of the estimator is evaluated using a global $\mathbb{L}^1$ risk and relying on the minimax approach. The assumptions made about the density are mild in the sense that $f$ may have some spatial variability, may not be bounded, continuous, compactly supported or in $\mathbb{L}^2$. The advantage of the method discussed is that it avoids the undesirable log factors that usually appear in older procedures. Particular attention is paid to assumptions about the tails of the distribution and their impact on the optimal estimation rates. New ones are thus revealed.
