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

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

TitleTesting for monotonicity of a regression mean by calibrating for linear functions
Publication TypeJournal Article
Year of Publication2000
AuthorsHall, P, Heckman, NE
JournalANNALS OF STATISTICS
Volume28
Pagination20-39
Date PublishedFEB
Type of ArticleArticle
ISSN0090-5364
Keywordsbootstrap, calibration, curve estimation, Monte Carlo, response curve, running gradient
AbstractA 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.