Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1150191 | Journal of Statistical Planning and Inference | 2007 | 13 Pages |
Abstract
Wavelet-based density estimators with randomly right-censored data are considered. We investigate the asymptotic rates of convergence of estimators based on thresholding of empirical wavelet coefficients. Unlike the complete data case, the empirical wavelet coefficients are constructed through the Kaplan-Meier estimators of the distribution functions. It turns out that these coefficients can be approximated by an average of i.i.d. random variables with a certain error rate. We show that the estimators achieve nearly optimal minimax convergence rates within logarithmic terms over a large range of Besov function classes Bpqα,α>1/p,p⩾1,q⩾1, a feature not available for linear estimators when p<2.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Linyuan Li,