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

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.