Monotonic regression for large multivariate datasets

Abstract: Monotonic regression is a non-parametric statistical method that is designed especially for applications in which the expected value of a response variable increases or decreases in one or more explanatory variables. Such applications can be found in business, physics, biology, medicine, signal processing, and other areas. Inasmuch as many of the collected datasets can contain a very large number of multivariate observations, there is a strong need for efficient numerical algorithms. Here, we present new methods that make it feasible to fit monotonic functions to more than one hundred thousand data points. By simulation, we show that our algorithms have high accuracy and represent  considerable improvements with respect to computational time and memory requirements. In particular , we demonstrate how segmentation of a large-scale problem can greatly improve the performance of existing algorithms. Moreover, we show how the uncertainty of a monotonic regression model can be estimated. One of the procedures we developed can be employed to estimate the variance of the random error present in the observed r(,'Sponse. Other procedures are ba.'led on resampling  techniques and can provide confidence intervals for the expected response at given levels of a set of predictors.