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Forests 2016, 7(9), 194; doi:10.3390/f7090194

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

1
Research Institute of Forest Resource Information Techniques, Chinese Academy of Forestry, Beijing 100091, China
2
Key Laboratory for Plant Diversity and Biogeography of East Asia, Kunming Institute of Botany, Chinese Academy of Sciences, Kunming 650201, Yunnan, China
3
Faculty of Forestry and Wood Sciences, Czech University of Life Sciences Prague, Prague 6, Czech Republic
4
Penn State Hershey Cancer Institute, Penn State College of Medicine, Hershey, PA 17033, USA
5
College of Computer and Information Techniques, Xinyang Normal University, Xinyang 464000, Henan, China
6
Center for Statistical Genetics, Pennsylvania State University, Loc T3436, Mailcode CH69, 500 University Drive, Hershey, PA 17033, USA
*
Author to whom correspondence should be addressed.
Academic Editors: Jean-Claude Ruel and Eric J. Jokela
Received: 21 July 2016 / Revised: 26 August 2016 / Accepted: 27 August 2016 / Published: 31 August 2016
View Full-Text   |   Download PDF [2978 KB, uploaded 1 September 2016]   |  

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. View Full-Text
Keywords: segmented taper equation; unconstrained least square regression; constrained two-dimensional optimum seeking; parameter estimation; precious tree species segmented taper equation; unconstrained least square regression; constrained two-dimensional optimum seeking; parameter estimation; precious tree species
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Pang, L.; Ma, Y.; Sharma, R.P.; Rice, S.; Song, X.; Fu, L. Developing an Improved Parameter Estimation Method for the Segmented Taper Equation through Combination of Constrained Two-Dimensional Optimum Seeking and Least Square Regression. Forests 2016, 7, 194.

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