Comparison of Regression Curves Using Quasi-Residuals

Abstract

We consider testing the equality of two regression functions using two independent samples. Three tests are proposed that are free of the restriction of having the same covariate values or sample sizes for both samples. Asymptotic distributions are given and results from a simulation study are presented that show the superior power properties of these tests over a competing test in a variety of cases, including the testing of hypotheses involving high-frequency curves when the design points for the two samples differ. It is also observed that the tests have good level properties when proper smoothing parameters are selected.

Key Words:

• Design variables
• Kernel estimator
• Nonparametric test