Kernels for nonparametric curve estimation. (English) Zbl 0574.62042

Gasser, T.; Müller, H.-G.; Mammitzsch, V.

J. R. Stat. Soc., Ser. B 47, 238-252 (1985).

The problem of kernel choice for nonparametric estimation of regression functions, probability densities and their derivatives is considered. The properties of the so-called minimum variance optimal kernels of order (\(\nu\),k), minimizing the asymptotic variance and the asymptotic integrated mean square error (IMSE), respectively, are studied.
The so-called boundary kernels are introduced for estimating at the extremities of the data. Some tables for the asymptotic bias, variance and IMSE for optimal and minimum variance kernels are given.

Reviewer: R.Mnatsakanov

MSC:

62G05

Nonparametric estimation

Keywords:

curve estimation; rate of convergence; density estimation; kernel choice; regression functions; derivatives; minimum variance optimal kernels; asymptotic variance; asymptotic integrated mean square error; boundary kernels; tables