Testing for the equality of two nonparametric regression curves

✍ Scribed by Hira L. Koul; Anton Schick

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 893 KB
• Volume: 65
• Category: Article
• ISSN: 0378-3758
• DOI: 10.1016/s0378-3758(97)00063-3

✦ Synopsis

This paper discusses the problem of testing the equality of two non-parametric regression curves against one-sided alternatives when the design points are common and when they are distinct. Two classes of tests are given for each case. One class of tests requires the estimation of the common regression function while the other class avoids this. This paper derives the asymptotic power of these tests for contiguous alternatives, obtains an upper bound on the asymptotic power of all tests under these alternatives and then discusses asymptotically optimal tests from these classes. As an example, in the distinct design case, a weighted covariate matched Wilcoxon Mann Whitney test turns out to be optimal against certain contingous alternatives if the error density is logistic. Optimal tests are also given at the normal error density. A simulation study investigates the behavior of these tests for moderate sample sizes. ~' 1997 Elsevier Science B.V.