Nonparametric comparison of several regression functions: Exact and asymptotic theory

• 成果类型: Article
• 署名作者: Munk, A; Dette, H
• 署名单位: Ruhr University Bochum; Ruhr University Bochum
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1998
• 页码: 2339-2368
• 关键词: residual variance; difference; EQUALITY; CURVES; MODEL

摘要

A new test is proposed for the comparison of two regression curves f and g. We prove an asymptotic normal law under fixed alternatives which can be applied for power calculations, for constructing confidence regions and for testing precise hypotheses of a weighted L-2 distance between f and g. In particular, the problem of nonequal sample sizes is treated, which is related to a peculiar formula of the area between two step functions. These results are extended in various directions, such as the comparison of k regression functions or the optimal allocation of the sample sizes when the total sample size is fixed. The proposed pivot statistic is not based on a nonparametric estimator of the regression curves and therefore does not require the specification of any smoothing parameter.