Translator Disclaimer
March, 1987 Variable Bandwidth Kernel Estimators of Regression Curves
Hans-Georg Muller, Ulrich Stadtmuller
Ann. Statist. 15(1): 182-201 (March, 1987). DOI: 10.1214/aos/1176350260


In the model $Y_i = g(t_i) + \varepsilon_i,\quad i = 1,\cdots, n,$ where $Y_i$ are given observations, $\varepsilon_i$ i.i.d. noise variables and $t_i$ nonrandom design points, kernel estimators for the regression function $g(t)$ with variable bandwidth (smoothing parameter) depending on $t$ are proposed. It is shown that in terms of asymptotic integrated mean squared error, kernel estimators with such a local bandwidth choice are superior to the ordinary kernel estimators with global bandwidth choice if optimal bandwidths are used. This superiority is maintained in a certain sense if optimal local bandwidths are estimated in a consistent manner from the data, which is proved by a tightness argument. The finite sample behavior of a specific local bandwidth selection procedure based on the Rice criterion for global bandwidth choice [Rice (1984)] is investigated by simulation.


Download Citation

Hans-Georg Muller. Ulrich Stadtmuller. "Variable Bandwidth Kernel Estimators of Regression Curves." Ann. Statist. 15 (1) 182 - 201, March, 1987.


Published: March, 1987
First available in Project Euclid: 12 April 2007

zbMATH: 0634.62032
MathSciNet: MR885731
Digital Object Identifier: 10.1214/aos/1176350260

Primary: 62G05
Secondary: 65D10, 65J02

Rights: Copyright © 1987 Institute of Mathematical Statistics


Vol.15 • No. 1 • March, 1987
Back to Top