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Characterizing prediction errors of a new tree height model for cut-to-length Pinus radiata stems through the Burr TypeⅫdistribution

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林业研究:英文版 2023年第6期34卷 1899-1914页

作者： Xinyu Cao Huiquan Bi Duncan Watt Yun Li School of Information Science and Technology Beijing Forestry UniversityBeijing 100083People’s Republic of China Forest Science NSW Department of Primary IndustriesLevel 304PSQParramattaNSW 2150Australia School of Ecosystem and Forest Sciences Faculty of ScienceThe University of MelbourneWater StreetCreswickVIC 3363Australia Snowy Region Forestry Corporation of NSW76 Capper StreetTumutNSW 2720Australia

Unlike height-diameter equations for standing trees commonly used in forest resources modelling,tree height models for cut-to-length(CTL)stems tend to produce prediction errors whose distributions are not conditionally normal but are rather leptokurtic and heavy-tailed.This feature was merely noticed in previous studies but never thoroughly investigated.This study characterized the prediction error distribution of a newly developed such tree height model for Pin us radiata(D.Don)through the three-parameter Burr TypeⅫ(BⅫ)distribution.The model’s prediction errors(ε)exhibited heteroskedasticity conditional mainly on the small end relative diameter of the top log and also on DBH to a minor extent.Structured serial correlations were also present in the data.A total of 14 candidate weighting functions were compared to select the best two for weightingεin order to reduce its conditional heteroskedasticity.The weighted prediction errors(εw)were shifted by a constant to the positive range supported by the BXII distribution.Then the distribution of weighted and shifted prediction errors(εw+)was characterized by the BⅫdistribution using maximum likelihood estimation through 1000 times of repeated random sampling,fitting and goodness-of-fit testing,each time by randomly taking only one observation from each tree to circumvent the potential adverse impact of serial correlation in the data on parameter estimation and inferences.The nonparametric two sample Kolmogorov-Smirnov(KS)goodness-of-fit test and its closely related Kuiper’s(KU)test showed the fitted BⅫdistributions provided a good fit to the highly leptokurtic and heavy-tailed distribution ofε.Random samples generated from the fitted BⅫdistributions ofεw+derived from using the best two weighting functions,when back-shifted and unweighted,exhibited distributions that were,in about97 and 95%of the 1000 cases respectively,not statistically different from the distribution ofε.Our results for cut-tolength P.radiata stems represented the first case of any tree species where

关键词： Conditional heteroskedasticity Leptokurtic error distribution Skedactic function Nonlinear quantile regression Weighted prediction errors Serial correlation Random sampling and fitting nonparametric goodnessof-fit tests

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