Testing for monotonicity of a regression mean by calibrating for linear functions

• 成果类型: Article
• 署名作者: Hall, P; Heckman, NE
• 署名单位: Australian National University; University of British Columbia
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2000
• 页码: 20-39
• 关键词: Nonparametric regression; residual variance; DENSITY-ESTIMATION; multimodality; CHOICE

摘要

A new approach to testing. for monotonicity of a regression mean, not requiring computation of a curve estimator or a bandwidth, is suggested. It is based on the notion of running gradients over short, intervals, although from some viewpoints it may be regarded as an analogue for monotonicity testing of the dip/excess mass approach for testing modality hypotheses about densities. Like the latter methods, the new technique does not suffer difficulties caused by almost-Bat parts of the target function. In fact, it is calibrated so as to work well for flat response curves, and as a result it has relatively good power properties in boundary cases where the curve exhibits shoulders. Ln this respect, as well as in its construction, the running gradients approach differs from alternative techniques based on the notion of a critical bandwidth.