Non-Euclidean locally monotonic regression
The concept of locally monotonic regression is extended by considering metrics on r/sup n/ that are different from the Euclidean metric. The existence of regressions for a large class of metrics is shown. Algorithms that show the computability of locally monotonic regressions are given. A general algorithm that computes regressions for the l/sub p/ metrics is given; considered in detail are the cases corresponding to the metrics l/sub 1/ and l/sub infinity /, where the sample median and the sample midrange play important roles.<<ETX>>