Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1155122 | Statistics & Probability Letters | 2008 | 5 Pages |
Abstract
Let (Xi)iâ¥1 be an i.i.d. sample on Rd having density f. Given a real function Ï on Rd with finite variation, and given an integer valued sequence (jn), let fËn denote the estimator of f by wavelet projection based on Ï and with multiresolution level equal to jn. We provide exact rates of almost certain convergence to 0 of the quantity supxâH|fËn(x)âE(fËn)(x)|, when n2âdjn/lognââ and H is a given hypercube of Rd. We then show that, if n2âdjn/lognâc for a constant c>0, then the quantity supxâH|fËn(x)âf| almost surely fails to converge to 0.
Related Topics
Physical Sciences and Engineering
Mathematics
Statistics and Probability
Authors
Davit Varron,