Statistics Seminar: Andrze Kozek -- Data sharpening by improved quantile estimators

Andrzej Stefan Kozek Department of Statistics Macquarie University 

Location: Carslaw 173 

Time: 2pm Friday, May 20, 2011 

Title: Data sharpening by improved quantile estimators 

Abstract: In probability density estimation the kernel method, despite its many
drawbacks, remains popular, next to histograms, because of its simplicity.  There exist
many approaches improving the original Parzen-Rozenblatt estimator, one of them has been
labelled as ’data sharpening’.  The data sharpening consists in replacing the original
data with slightly corrected ’sharpened data’.  This correction results in reduction of
bias of kernel estimators of the probability density function.  We show that properly
chosen nonparametric estimators of (i/(n+1))-quantiles can serve as the sharpened data
and in simulations on average they consistently outperform the original estimator with
the Sheather-Jones-Hall-Marron smoothing parameter.