Multivariate isotonic regression and its algorithms

Abstract

We use regression functions, which are the means of random variables, to interpret statistical inference. Often an order is imposed on the values of the regression function. Thus, we refer to the regression as an order restricted regression or an isotonic regression. In this paper we explain how to calculate multivariate isotonic regression. However, we investigate the case for a particular restriction on our elements. We impose relations between elements of the same row but not between rows. The technique is to decompose our multivariate model into univariate models so that prior knowledge about the simpler case can be used. Finally, we propose an algorithm to calculate multivariate isotonic regression. This algorithm could then be converted into a computer program.