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On kernel density estimation near endpoints

✍ Scribed by Shunpu Zhang; Rohana J. Karunamuni

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 144 KB
Volume: 70
Category: Article
ISSN: 0378-3758
DOI: 10.1016/s0378-3758(97)00187-0

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✦ Synopsis

In this paper, we consider the estimation problem of f(0), the value of density f at the left endpoint 0. Nonparametric estimation of f( 0) is rather formidable due to boundary e ects that occur in nonparametric curve estimation. It is well known that the usual kernel density estimates require modiÿcations when estimating the density near endpoints of the support. Here we investigate the local polynomial smoothing technique as a possible alternative method for the problem. It is observed that our density estimator also possesses desirable properties such as automatic adaptability for boundary e ects near endpoints. We also obtain an 'optimal kernel' in order to estimate the density at endpoints as a solution of a variational problem. Two bandwidth variation schemes are discussed and investigated in a Monte Carlo study.

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