FITTING MONOTONIC POLYNOMIALS TO DATA

Many statistical applications require fitting a general monotonic function to data. These applications range from regular nonlinear regression modeling there the response is known to be monotonic, through transformations of data to normality, to work-horse routines in nonmetric scaling procedures. Monotonic polynomials comprise a class of possible monotonic functions for this. Offsetting their well-known drawbacks of poor extrapolatory properties and proclivity to tax the numerical accuracy of fitting algorithms, they have many advantages. They are parsimonious, provide predictions that vary smoothly with the argument, and are able to approximate any smooth function to arbitrary accuracy. This paper presents a procedure for fitting monotonic polynomials and illustrates their use in conventional regression modeling and in data transformation.