Developing an Improved Parameter Estimation Method for the Segmented Taper Equation through Combination of Constrained Two-Dimensional Optimum Seeking and Least Square Regression

Abstract

The segmented taper equation has great flexibility and is widely applied in exiting taper systems. The unconstrained least square regression (ULSR) was generally used to estimate parameters in previous applications of the segmented taper equations. The joint point parameters estimated with ULSR may fall outside the feasible region, which leads to the results of the segmented taper equation being uncertain and meaningless. In this study, a combined method of constrained two-dimensional optimum seeking and least square regression (CTOS & LSR) was proposed as an improved method to estimate the parameters in the segmented taper equation. The CTOS & LSR was compared with ULSR for both individual tree-level equation and the population average-level equation using data from three tropical precious tree species (Castanopsis hystrix, Erythrophleum fordii, and Tectona grandis) in the southwest of China. The differences between CTOS & LSR and ULSR were found to be significant. The segmented taper equation estimated using CTOS & LSR resulted in not only increased prediction accuracy, but also guaranteed the parameter estimates in a more meaningful way. It is thus recommended that the combined method of constrained two-dimensional optimum seeking and least square regression should be a preferred choice for this application. The computation procedures required for this method is presented in the article.