Sequential design for local bandwidth response curve estimator

Abstract

Suppose we want to estimate the response curve using a kernel estimator. When we perform an experiment to estimate the response curve, we usually decide on the location of all the design points in advance of the experiment. Müller and Schmitt (1988) propose the optimal design, but in practice, we need some prior information about response curve to construct such a design. Park and Faraway (1998) present the sequential design for the global bandwidth estimator and show that their sequential design is asymptotically equivalent to the optimal design and is more efficient than the evenly spaced design. However, the sequential design points will be unequally spaced and so using a global bandwidth may not be appropriate. In this paper, we present the sequential design for the local bandwidth response curve estimator.

Keywords:

• Nonparametric kernel regression
• response curve
• local bandwidth choice
• sequential design