TY - JOUR
T1 - Effective interpolations for kernel density estimators
AU - Kogure, Atsuyuki
PY - 1998/1/1
Y1 - 1998/1/1
N2 - In this paper we introduce a general interpolation scheme to be applied in the kernel density estimation. Our scheme is based on a piecewise higher-degree polynomial interpolation with a strategically chosen set of interpolation points. It is found that our interpolation scheme improves on the kernel density estimation in terms of the integrated mean squared error. A multivariate extension of our findings shows that the improvement increases substantially with the data dimension. In addition to the theoretical improvement, it is demonstrated that our interpolation scheme brings about a considerable computational saving over the original kernel density estimator, making itself comparable to the binning technique in the computational efficiency.
AB - In this paper we introduce a general interpolation scheme to be applied in the kernel density estimation. Our scheme is based on a piecewise higher-degree polynomial interpolation with a strategically chosen set of interpolation points. It is found that our interpolation scheme improves on the kernel density estimation in terms of the integrated mean squared error. A multivariate extension of our findings shows that the improvement increases substantially with the data dimension. In addition to the theoretical improvement, it is demonstrated that our interpolation scheme brings about a considerable computational saving over the original kernel density estimator, making itself comparable to the binning technique in the computational efficiency.
KW - Binned kernel estimator
KW - Higher-degree polynomial interpolation
KW - Higher-order kernel
KW - Multivariate interpolation
KW - Variance reduction
UR - http://www.scopus.com/inward/record.url?scp=0343863914&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0343863914&partnerID=8YFLogxK
U2 - 10.1080/10485259808832741
DO - 10.1080/10485259808832741
M3 - Article
AN - SCOPUS:0343863914
VL - 9
SP - 165
EP - 195
JO - Journal of Nonparametric Statistics
JF - Journal of Nonparametric Statistics
SN - 1048-5252
IS - 2
ER -