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

Series: 
Stochastics Seminar
Thursday, March 11, 2010 - 15:00
1 hour (actually 50 minutes)
Location: 
Skiles 269
,  
University of Connecticut
 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.