Curve fitting: a method of joining piecewise functions to produce models of complex data

Abstract

This article describes a method of curve-fitting that involves splitting the curve into two (or more) and creating separate functions for each part. These functions are then concatenated via a linking function to create one overall function that better describes the original data than is otherwise achievable. The linking function is able to do this by separating the original two functions so that they are each active in only the relevant portion of the overall curve without the use of dummy variables. The final result is a continuous function in which it is straightforward to smooth the transition at the knot between the piecewise subfunctions. In addition, the piecewise subfunctions do not need to align at the knot since the degree of smoothing is readily controlled. All types of functions may be concatenated so that the method is flexible and relatively simple to apply.

Keywords:

• Continuous function
• Curve fitting
• Hinge
• Knot
• modeling
• Piecewise functions
• Spline regression