Kernel density estimators are important tools for exploring and analyzing data distributions (see the references in Salgado-
Ugarte et al. 1993). However, one drawback of these procedures is the large number of calculations required to compute them.
As a consequence, it can be time consuming to compute kernel density estimators even for moderate sample sizes and when using
fast processors. Scott (1985) suggested an alternative procedure to overcome this problem: the Averaged S hifted Histogram
(ASH). Subsequently, Hardle and Scott (1988) developed a more general framework called WARPing (weighted averaging of
rounded points).
This insert, based mainly on some chapters from the books by Hardle (1991) and Scott (1992), briefly introduces the ASH
and WARPing procedures for density estimation and presents some ado-files and Turbo Pascal programs for their calculation.