Bivariate Isotonic Regression by Dynamic Programming

Abstract

This article extends the dynamic programming framework introduced by (Rote, 2019) from the univariate to the bivariate isotonic problem, using an anti-diagonal traversal procedure. The proposed algorithm is applied to the well-known baseball data set that describes the association of salary with a collection of player properties, including the number of runs batted and hits. The new algorithm is relevant in the sense that dynamic programming has a wide range of applications in economics, such as the savings problem, economic growth, job search, business cycles, oligopoly equilibrium, recursive contracts, and forecasting.