@article { ISI:000088077700002,
	title = {Testing for monotonicity of a regression mean by calibrating for linear functions},
	journal = {ANNALS OF STATISTICS},
	volume = {28},
	number = {1},
	year = {2000},
	month = {FEB},
	pages = {20-39},
	publisher = {INST MATHEMATICAL STATISTICS},
	type = {Article},
	address = {IMS BUSINESS OFFICE-SUITE 7, 3401 INVESTMENT BLVD, HAYWARD, CA 94545 USA},
	abstract = {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 {\textquoteleft}{\textquoteleft}running gradients{\textquoteright}{\textquoteright} 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 {\textquoteleft}{\textquoteleft}running gradients{\textquoteright}{\textquoteright} approach differs from alternative techniques based on the notion of a critical bandwidth.},
	keywords = {bootstrap, calibration, curve estimation, Monte Carlo, response curve, running gradient},
	issn = {0090-5364},
	author = {Hall, P and Heckman, NE}
}
