Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Convergence rates for pointwise curve estimation with a degenerate design

Abstract : The nonparametric regression with a random design model is considered. We want to recover the regression function at a point x where the design density is vanishing or exploding. Depending on assumptions on the regression function local regularity and on the design local behaviour, we find several minimax rates. These rates lie in a wide range, from slow l(n) rates where l(.) is slowly varying (for instance (log n)^(-1)) to fast n^(-1/2) * l(n) rates. If the continuity modulus of the regression function at x can be bounded from above by a s-regularly varying function, and if the design density is b-regularly varying, we prove that the minimax convergence rate at x is n^(-s/(1+2s+b)) * l(n).
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

Cited literature [14 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00003086
Contributor : Stéphane Gaïffas <>
Submitted on : Friday, January 13, 2006 - 9:43:13 PM
Last modification on : Saturday, March 28, 2020 - 2:11:29 AM
Long-term archiving on: : Thursday, September 23, 2010 - 3:59:57 PM

Identifiers

Citation

Stéphane Gaiffas. Convergence rates for pointwise curve estimation with a degenerate design. 2006. ⟨hal-00003086v3⟩

Share

Metrics

Record views

230

Files downloads

198