非参数估计在构造树高曲线中的应用

Application of nonparametric estimation method in establishing height-diameter curves of trees

研究测树因子之间的数学关系,是森林调查的重要理论工作.该文以树高曲线模型为例,首先分析了最小二乘估计(LS估计)存在的缺陷,然后采用非参数核密度估计和最大概率估计两种方法建立了树高曲线模型.结果表明:①核密度估计能在一定最优准则下很好地适应样本,误差小,样本的统计特性和多峰形态亦得到很好的反映;②最大概率估计则适合在因变量和自变量均有误差的情况下建立模型.它摈弃了LS估计和核密度估计只考虑因变量统计误差的局限性,因此这种估计方法更符合实际情况.同时,当样本中含有误差很大的异常数据时,核密度估计和最大概率估计所得模型比LS估计方法所得模型更稳定.

The study of mathematical relationships among forest measurements is an important theoretical principle in forest surveys. This paper presented several methods of the establishment of height-diameter curves of trees. First, some shortcomings of LS method were analyzed. Then two methods, nonparametric kernel density estimation and maximum likelihood estimation, were applied to survey data in order to establish models. From this study, the authors make the following two inferences： 1 ） kernel density estimation is well suited to fit samples under certain optimum conditions with minimum errors and also maintains its statistical characteristics and multiple peaks; 2） maximum likelihood estimation is appropriate in cases where both independent as well as dependent variables are subject to measurement errors. This overcomes the deficiency of LS estimation which only considers errors in the dependent variables and is therefore more in tune with practical experience. At the same time, both methods, kernel density and maximum likelihood estimation, are more suitable than LS estimation method in the case of outliers.