Comparison of two response curve estimators

Abstract

We compare the finite sample behavior of the local linear regression smoother and the Gasser and Müller estimator using a simulation study. To compare the performance of two estimators, we need the optimal design density for each estimator. For Gasser and Müller estimator, Müller and Schmitt (1988) derived the optimal design density. We describe the optimal design density for the local linear regression smoother. Even though the large sample properties of two estimators are identical, the small sample behaviors of two estimators turn out to be quite different.

Keywords:

• Gasser and Müller estimator
• local linear regression smoother
• response curve
• fixed design