## Needlet construction and geometric statistical rates

- March 15, 2011
- 1:30 p.m.
- LeConte 312

## Abstract

From the experience of the last years, we know that estimating a nonparametric (or very high dimensional) object from a small amount of data is possible, if we have sparsity *a priori* assumptions.
In some situations, the geometric analysis of the problem could help to build a suitable “dictionary” (here : a tight frame), on which this sparsity has a ‘natural meaning’ (for instance Besov conditions). In the first part of these two talks we will investigate statistical examples such as density estimation (or devonvolution on the sphere) or tomography, where the dimension clearly shows up in the rates of convergence. We will also detail how inverse problem aspects can influence the rates. We will gradually introduce problems where the rates show different types of ‘dimensions’ varying along the situations and difficult to explain.