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Ds-optimal designs for Kozak's tree taper model
Wondo Genet College of Forestry and Natural Resources, Hawassa University, Awassa, Ethiopia.
Umeå University, Faculty of Social Sciences, Department of Statistics.
2011 (English)In: Journal of Applied Statistics, ISSN 0266-4763, E-ISSN 1360-0532, Vol. 38, no 5, 1087-1102 p.Article in journal (Refereed) Published
Abstract [en]

In this work, we study Ds-optimal design for Kozak's tree taper model. The approximate Ds-optimal designs are found invariant to tree size and hence create a ground to construct a general replication-free Ds-optimal design. Even though the designs are found not to be dependent on the parameter value p of the Kozak's model, they are sensitive to the stimes1 subset parameter vector values of the model. The 12 points replication-free design (with 91% efficiency) suggested in this study is believed to reduce cost and time for data collection and more importantly to precisely estimate the subset parameters of interest.

Place, publisher, year, edition, pages
2011. Vol. 38, no 5, 1087-1102 p.
Keyword [en]
locally optimal design, Ds-optimal design, replication-free design, tree taper data, Kozak model
National Category
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-42812DOI: 10.1080/02664761003759925ISI: 000288373500018OAI: oai:DiVA.org:umu-42812DiVA: diva2:410451
Note

Originally included in thesis in manuscript form.

Available from: 2011-04-13 Created: 2011-04-13 Last updated: 2017-01-18Bibliographically approved
In thesis
1. Statistical modeling and design in forestry: The case of single tree models
Open this publication in new window or tab >>Statistical modeling and design in forestry: The case of single tree models
2008 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Forest quantification methods have evolved from a simple graphical approach to complex regression models with stochastic structural components. Currently, mixed effects models methodology is receiving attention in the forestry literature. However, the review work (Paper I) indicates a tendency to overlook appropriate covariance structures in the NLME modeling process.

A nonlinear mixed effects modeling process is demonstrated in Paper II using Cupressus lustanica tree merchantable volume data and compared several models with and without covariance structures. For simplicity and clarity of the nonlinear mixed effects modeling, four phases of modeling were introduced. The nonlinear mixed effects model for C. lustanica tree merchantable volume with the covariance structures for both the random effects and within group errors has shown a significant improvement over the model with simplified covariance matrix. However, this statistical significance has little to explain in the prediction performance of the model.

In Paper III, using several performance indicator statistics, tree taper models were compared in an effort to propose the best model for the forest management and planning purpose of the C. lustanica plantations. Kozak's (1988) tree taper model was found to be the best for estimating C. lustanica taper profile.

Based on the Kozak (1988) tree taper model, a Ds optimal experimental design study is carried out in Paper IV. In this study, a Ds-optimal (sub) replication free design is suggested for the Kozak (1988) tree taper model.

Place, publisher, year, edition, pages
Umeå: Statistik, 2008. 22 p.
Series
Statistical studies, ISSN 1100-8989 ; 1100-8989
Keyword
Forest data, Covariance structures, Nonlinear mixed effects models, Tree taper models, Ds-optimal design, Replication-free design.
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:umu:diva-1663 (URN)978-91-7264-501-1 (ISBN)
Public defence
2008-08-14, Lecture hall C, Samhällsvetarhuset, Umeå University, Umeå, 10:15
Opponent
Supervisors
Available from: 2008-05-16 Created: 2008-05-16 Last updated: 2017-01-18Bibliographically approved

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Arnoldsson, Göran

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