Computational Statistics (2006) 21:589–601 DOI 10.1007/s00180-006-0016-x O R I G I NA L PA P E R
A bias reducing technique in kernel distribution function estimation Choongrak Kim · Sungsoo Kim · Mira Park · Hakbae Lee
Published online: 4 November 2006 © Springer-Verlag 2006
Abstract In this paper we suggest a bias reducing technique in kernel distribution function estimation. In fact, it uses a convex combination of three kernel estimators, and it turned out that the bias has been reduced to the fourth power of the bandwidth, while the bias of the kernel distribution function estimator has the second power of the bandwidth. Also, the variance of the proposed estimator remains at the same order as the kernel distribution function estimator. Numerical results based on simulation studies show this phenomenon, too. Keywords Bandwidth · Bias · Convex combination · Kernel
1 Introduction As an estimator of distribution function, empirical distribution function estimator for the complete data or the Kaplan–Meier estimator (Kaplan and Meier 1958) for the censored data is widely used. But, these estimators are step functions, and therefore, they have undesirable properties. To overcome these disadvantages, smoothing versions of them are often used. Among them
C. Kim (B) · S. Kim Department of Statistics, Pusan National University, Pusan 609-735, South Korea e-mail:
[email protected] M. Park School of Medicine, Eulji University, Taejeon 301-832, South Korea H. Lee Department of Applied Statistics, Yonsei University, Seoul 120-749, South Korea
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kernel smoothing is most widely used because it is easy to derive and has good properties. Kernel smoothing has received a lot of attention in density estimation