Hasse diagrams and the generalized PAV-algorithm for monotonic regression in several explanatory variables

• Monotonic regression is a nonparametric method for estimation ofmodels in which the expected value of a response variable y increases ordecreases in all coordinates of a vector of explanatory variables x = (x1, …, xp).Here, we examine statistical and computational aspects of our recentlyproposed generalization of the pool-adjacent-violators (PAV) algorithm fromone to several explanatory variables. In particular, we show how the goodnessof-fit and accuracy of obtained solutions can be enhanced by presortingobserved data with respect to their level in a Hasse diagram of the partial orderof the observed x-vectors, and we also demonstrate how these calculations canbe carried out to save computer memory and computational time. Monte Carlosimulations illustrate how rapidly the mean square difference between fittedand expected response values tends to zero, and how quickly the mean squareresidual approaches the true variance of the random error, as the number of observations increases up to 104.

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Keyword

MATHEMATICS

MATEMATIK

Publication and Content Type

ref (subject category)

art (subject category)