My. Cheng, BOUNDARY AWARE ESTIMATORS OF INTEGRATED DENSITY DERIVATIVE PRODUCTS, Journal of the Royal Statistical Society. Series B: Methodological, 59(1), 1997, pp. 191-203
Citations number
20
Categorie Soggetti
Statistic & Probability","Statistic & Probability
Journal title
Journal of the Royal Statistical Society. Series B: Methodological
Integrated squared density derivatives are important to the plug-in ty
pe of bandwidth selector for kernel density estimation. Conventional e
stimators of these quantities are inefficient when there is a non-smoo
th boundary in the support of the density. We introduce estimators tha
t utilize density derivative estimators obtained from local polynomial
fitting. They retain the rates of convergence in mean-squared error t
hat are familiar from non-boundary cases, and the constant coefficient
s have similar forms. The estimators and the formula for their asympto
tically optimal bandwidths, which depend on integrated products of den
sity derivatives, are applied to automatic bandwidth selection for loc
al linear density estimation. Simulation studies show that the constru
cted bandwidth rule and the Sheather-Jones bandwidth are competitive i
n non-boundary cases, but the former overcomes boundary problems where
as the latter does not.