Uniform limit theorems for wavelet density estimators and adaptive estimation of densities

Stochastics Seminar
Thursday, March 11, 2010 - 3:00pm for 1 hour (actually 50 minutes)
Skiles 269
Evarist GinĂ© – University of Connecticut
Yuri Bakhtin
The almost sure rate of convergence in the sup norm for linear wavelet density estimators is obtained, as well as a central limit theorem for the distribution functions based on these estimators. These results are then applied to show that the hard thresholding wavelet estimator of Donoho, Johnstone, Kerkyacharian and Picard (1995) is adaptive in sup norm to the smoothness of a density. An alternative adaptive estimator combining Lepski's method with Rademacher complexities will also be described. This is joint work with Richard Nickl.