A comprehensive comparison of algorithms for the statistical modelling of non-monotone relationships via isotonic regression of transformed data

Abstract

The paper treats the problem of nonlinear, non-monotonic regression of bivariate datasets by means of a statistical regression method known from the literature. In particular, the present paper introduces two new regression methods and illustrates the results of a comprehensive comparison of the performances of the best two previous methods, the two new methods introduced here and as much as ten standard regression methods known from the specialised literature. The comparison is performed over nine different datasets, ranging from electrocardiogram data to text analysis data, by means of four figures of merit, that include regression precision as well as runtime.