Statistics

    

Minimum with Inequality Constraint Applied to Increasing Cubic, Logistic and Gomperz or Convex Quartic and Biexponential Regressions

Authors: Josef Bukac

We present a method of minimizing an objective function subject to an inequality constraint. It enables us to minimize the sum of squares of deviations in linear regression under inequality restrictions. We demonstrate how to calculate the coefficients of cubic function under the restriction that it is increasing, we also mention how to fit a convex quartic polynomial. We use such results for interpolation as a method for calculation of starting values for iterative methods of fitting some specific functions, such as four-parameter logistic, positive bi-exponential, or Gomperz functions. Curvature-driven interpolation enables such calculations for otherwise solutions to interpolation equations may not exist or may not be unique. We also present examples to illustrate how it works and compare our approach with that of Zhang (2020).

Comments: 28 Pages.

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Submission history

[v1] 2021-12-02 02:52:21

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