Estimating composite functions by model selection

Details Estimating composite functions by model selection Estimating composite functions by model selection

2011-02-14

arxiv.org/abs/1102.2818v1

Mathematics

Statistics Theory

35 pages

Scientific paper

We consider the problem of estimating a function $s$ on $[-1,1]^{k}$ for large values of $k$ by looking for some best approximation by composite functions of the form $g\circ u$. Our solution is based on model selection and leads to a very general approach to solve this problem with respect too many different types of functions $g,u$ and statistical frameworks. In particular, we handle the problems of approximating $s$ by additive functions, single and multiple index models, neural networks, mixtures of Gaussian densities (when $s$ is a density) among other examples. We also investigate the situation where $s=g\circ u$ for functions $g$ and $u$ belonging to possibly anisotropic smoothness classes. In this case, our approach leads to a completely adaptive estimator with respect to the regularity of $s$.

Affiliated with

Also associated with

No associations

Rating

Estimating composite functions by model selection does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Estimating composite functions by model selection, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Estimating composite functions by model selection will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-216575