密度—直径关系研究中变量变换形式的选择和变量误差矩阵的估计

The Choice of Variables Transformation and Estimate of Measurement Error Matrix for the Study on Density diameter Relationship

在林分自稀疏过程研究中，利用度量误差模型的形式估计林分断面积平均直径Ｄｇ与单位面积株数Ｎ关系模型的参数时，需要确定Ｄｇ和Ｎ的抽样误差ｅ、ε方差的比值。本文利用２０块人工落叶松标地的材料，经过再抽样，计算并比较了各种数据变换方式下，断面积平均直径与单位面积株数的方差比。结果表明ｌｎ（Ｎ）和Ｄｇ的方差比接近于常数，其均值为３．０２４８×１０－２。由此，可确定变量的变换形式和构造误差矩阵，从而为精确估计模型参数提供依据。

It is necessary to determine the ratio between variance of sampling error e of quadratic average diameter Dg and that of sampling error ε of the tree numbers N per unit area when measurement error models is applied to estimate the parameters of a model between Dg and N ,in a study on stand self thinning processes.This paper calculated and compared the variance ratios between transformd quadratic average diameter and transformd number of trees per unit area by using resampling from 20 larch plantation plots.The results show that the ratio between variance of ln( N ) and Dg approaches to a constant 3.024 8 ×10 2 . From the results,the best form of variable transformation is determined and the structure of error matrix is constructed,which can be used to get more accurate estimate of model parameters.