Applications of the Discrete Least Squares 3-Convex Fit To Sigmoid Data

Let data of a univariate process be given. If the data are related by a sigmoid curve, but the sigmoid property has been lost due to the errors of the measuring process, then the least sum of squares change to the data that provides nonnegative third divided differences may be required. It is a structured quadratic programming calculation, which is solved very efficiently by a special least squares algorithm that takes into account the form of the constraints. The algorithm is outlined and two examples on real economic data are considered. The first is an application to the U.S.A. renewable energy consumption data during the period 1980-2010, which exhibit a sigmoid pattern. The second is an application to technological substitutions among the PDP computers to the VAX computers between the years 1984 and 1991. The results are briefly analyzed and the modeling capability of the method is demonstrated.