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--- seminars:stat:160218 [2016/03/01 16:49] – shang
+++ seminars:stat:160218 [2016/05/02 01:47] (current) – aleksey
@@ Line 1: / Line 1: @@
+<WRAP centeralign>##Statistics Seminar##\\ Department of Mathematical Sciences</WRAP>
+~~META:title =February 18, 2016~~
+<WRAP 70% center>
+^  **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 |
+</WRAP>
+\\
+<WRAP center box 80%>
+<WRAP centeralign>**Abstract**</WRAP>
+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 $n^{-1/2}$.
+</WRAP>