This study was conducted to evaluate the performance of the four stem taper models on Camellia japonica in Jeju Island, Korea using fit statistics and lack-of-fit statistics. The five statistical criteria that were us...This study was conducted to evaluate the performance of the four stem taper models on Camellia japonica in Jeju Island, Korea using fit statistics and lack-of-fit statistics. The five statistical criteria that were used in this study were standard error of estimate(SEE), mean bias( E), absolute mean difference(AMD), coefficient of determination(R2), and root mean square error(RMSE). Results showed that the Kozak model 02 stem taper had the best performance in all fit statistics(SEE: 3.4708, E : 0.0040 cm, AMD : 0.9060 cm, R2 : 0.9870, and RMSE : 1.2545). On the other hand, Max and Burkhart stem taper model had the poorest performance in each statistical criterion(SEE: 4.2121, E : 0.2520 cm, AMD : 1.1300 cm, R2 : 0.9805, and RMSE: 1.5317). For the lack-of-fit statistics, the Kozak model 02 also provided the best performance having the best AMD in most of the relative height classes for diameter outside bark prediction and in most of the DBH classes for total volume prediction while Max and Burkhart had the poorest performance. These stem taper equations could help forest managers to better estimate the diameter outside bark at any given height, merchantable stem volumes and total stem volumes of the standing trees of Camellia japonica in the forests of Jeju Island, Korea.展开更多
Relative error rather than the error itself is of the main interest in many practical applications. Criteria based on minimizing the sum of absolute relative errors （MRE） and the sum of squared relative errors （RLS...Relative error rather than the error itself is of the main interest in many practical applications. Criteria based on minimizing the sum of absolute relative errors （MRE） and the sum of squared relative errors （RLS） were proposed in the different areas. Motivated by K. Chen et al.＇s recent work [J. Amer. Statist. Assoc., 2010, 105： 1104-1112] on the least absolute relative error （LARE） estimation for the accelerated failure time （AFT） model, in this paper, we establish the connection between relative error estimators and the M-estimation in the linear model. This connection allows us to deduce the asymptotic properties of many relative error estimators （e.g., LARE） by the well-developed M-estimation theories. On the other hand, the asymptotic properties of some important estimators （e.g., MRE and RLS） cannot be established directly. In this paper, we propose a general relative error criterion （GREC） for estimating the unknown parameter in the AFT model. Then we develop the approaches to deal with the asymptotic normalities for M-estimators with differentiable loss functions on R or R／{0} in the linear model. The simulation studies are conducted to evaluate the performance of the proposed estimates for the different scenarios. Illustration with a real data example is also provided.展开更多
基金support of the Warm Temperate and Subtropical Forest Research Center, Korea Forest Research Institute
文摘This study was conducted to evaluate the performance of the four stem taper models on Camellia japonica in Jeju Island, Korea using fit statistics and lack-of-fit statistics. The five statistical criteria that were used in this study were standard error of estimate(SEE), mean bias( E), absolute mean difference(AMD), coefficient of determination(R2), and root mean square error(RMSE). Results showed that the Kozak model 02 stem taper had the best performance in all fit statistics(SEE: 3.4708, E : 0.0040 cm, AMD : 0.9060 cm, R2 : 0.9870, and RMSE : 1.2545). On the other hand, Max and Burkhart stem taper model had the poorest performance in each statistical criterion(SEE: 4.2121, E : 0.2520 cm, AMD : 1.1300 cm, R2 : 0.9805, and RMSE: 1.5317). For the lack-of-fit statistics, the Kozak model 02 also provided the best performance having the best AMD in most of the relative height classes for diameter outside bark prediction and in most of the DBH classes for total volume prediction while Max and Burkhart had the poorest performance. These stem taper equations could help forest managers to better estimate the diameter outside bark at any given height, merchantable stem volumes and total stem volumes of the standing trees of Camellia japonica in the forests of Jeju Island, Korea.
文摘Relative error rather than the error itself is of the main interest in many practical applications. Criteria based on minimizing the sum of absolute relative errors （MRE） and the sum of squared relative errors （RLS） were proposed in the different areas. Motivated by K. Chen et al.＇s recent work [J. Amer. Statist. Assoc., 2010, 105： 1104-1112] on the least absolute relative error （LARE） estimation for the accelerated failure time （AFT） model, in this paper, we establish the connection between relative error estimators and the M-estimation in the linear model. This connection allows us to deduce the asymptotic properties of many relative error estimators （e.g., LARE） by the well-developed M-estimation theories. On the other hand, the asymptotic properties of some important estimators （e.g., MRE and RLS） cannot be established directly. In this paper, we propose a general relative error criterion （GREC） for estimating the unknown parameter in the AFT model. Then we develop the approaches to deal with the asymptotic normalities for M-estimators with differentiable loss functions on R or R／{0} in the linear model. The simulation studies are conducted to evaluate the performance of the proposed estimates for the different scenarios. Illustration with a real data example is also provided.
