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.