##Statistics Seminar##\\ Department of Mathematical Sciences
~~META:title =February 18, 2016~~
^ **DATE:**|Thursday, February 18, 2016 |
^ **TIME:**|1:15pm to 2:15pm |
^ **LOCATION:**|WH 100E |
^ **SPEAKER:**|Anton Schick, Binghamton University |
^ **TITLE:**|Convergence rates of kernel density estimators in the $L_1$ norm |
\\
**Abstract**
The usual approach to evaluate the performance of a kernel density
estimator (KDE) is to look at the mean integrated square error.
This provides rates of convergence in the $L_2$-norm.
In this talk rates of convergence in the $L_1$-norm are presented.
We consider both estimators of a density $f$ and its convolution $f*f$ with itself.
In the former case the rates are nonparametric $n^{-s/(2s+1)}$
and depend on the smoothness $s$ of $f$. In the second case we obtain
the parametric rate $n^{-1/2}$.