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seminars:stat:160218

Statistics Seminar
Department of Mathematical Sciences

 DATE: Thursday, February 18, 2016 1:15pm to 2:15pm WH 100E Anton Schick, Binghamton University 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 $n^{-1/2}$.