Dl.1 Non-Euclidean Locally Monotonic Regression

The recently introduced concept of locally monotonic regression (l) is extended by considering metrics on Rn that are different from the Euclidean metric. We show the existence of regressions for a large class of metrics. Algorithms that show the computablity of locally monotonic regressions are given. A general algorithm that computes regressions for the Ip metrics is given: considered in detail are the cases corresponding to the metrics 11 and I,, where the sample median and the sample midrange play important roles.