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Additive isotonic regression attempts to determine the relationship between amulti-dimensional observation variable and a response, under the constraintthat the estimate is the additive sum of univariate component effects that aremonotonically increasing. In this article, we present a new method for suchregression called LASSO Isotone (LISO). LISO adapts ideas from sparse linearmodelling to additive isotonic regression. Thus, it is viable in manysituations with high dimensional predictor variables, where selection ofsignificant versus insignificant variables are required. We suggest analgorithm involving a modification of the backfitting algorithm CPAV. We give anumerical convergence result, and finally examine some of its propertiesthrough simulations. We also suggest some possible extensions that improveperformance, and allow calculation to be carried out when the direction of themonotonicity is unknown.

LASSO ISOtone for High Dimensional Additive Isotonic Regression