4 papers
Pointwise convergence of purely random partition estimators: from random trees to prototype rules
Jérémy Bettinger, François Portier, Adrien Saumard
We study pointwise convergence rates of purely random partition estimators in nonparametric regression, where the partition -- into hyper-rectangles by purely random trees, or into…
Revisiting local regression: shape regularity, uniform rates, and the limits of random splits
Jérémy Bettinger, François Portier, Adrien Saumard
Considering pointwise and sup-norm estimation, we analyze the non-asymptotic behavior of local averaging estimators for Lipschitz regression functions. Building on a general deviat…
On the pointwise and sup-norm errors for local regression estimators
Jérémy Bettinger, François Portier, Adrien Saumard
In this paper, we analyze the behavior of various non-parametric local regression estimators, i.e. estimators that are based on local averaging, for estimating a Lipschitz regressi…
A theory of shape regularity for local regression maps
Jérémy Bettinger, François Portier, Adrien Saumard
We introduce the concept of shape-regular regression maps as a framework to derive optimal rates of convergence for various non-parametric local regression estimators. Using Vapnik…