In this article, authors introduce a method to assess local influence of obser- vations on the parameter estimates and prediction in multivariate regression model. The diagnostics under the perturbations of error vari...In this article, authors introduce a method to assess local influence of obser- vations on the parameter estimates and prediction in multivariate regression model. The diagnostics under the perturbations of error variance, response variables and explanatory variables are derived, and the results are compared with those of case- deletion. Two examples are analyzed for illustration.展开更多
Recursive algorithms are very useful for computing M-estimators of regression coefficients and scatter parameters. In this article, it is shown that for a nondecreasing ul （t）, under some mild conditions the recursi...Recursive algorithms are very useful for computing M-estimators of regression coefficients and scatter parameters. In this article, it is shown that for a nondecreasing ul （t）, under some mild conditions the recursive M-estimators of regression coefficients and scatter parameters are strongly consistent and the recursive M-estimator of the regression coefficients is also asymptotically normal distributed. Furthermore, optimal recursive M-estimators, asymptotic efficiencies of recursive M-estimators and asymptotic relative efficiencies between recursive M-estimators of regression coefficients are studied.展开更多
Background: Leaf Area Index(LAI) is an important parameter used in monitoring and modeling of forest ecosystems. The aim of this study was to evaluate performance of the artificial neural network(ANN) models to predic...Background: Leaf Area Index(LAI) is an important parameter used in monitoring and modeling of forest ecosystems. The aim of this study was to evaluate performance of the artificial neural network(ANN) models to predict the LAI by comparing the regression analysis models as the classical method in these pure and even-aged Crimean pine forest stands.Methods: One hundred eight temporary sample plots were collected from Crimean pine forest stands to estimate stand parameters. Each sample plot was imaged with hemispherical photographs to detect the LAI. The partial correlation analysis was used to assess the relationships between the stand LAI values and stand parameters, and the multivariate linear regression analysis was used to predict the LAI from stand parameters. Different artificial neural network models comprising different number of neuron and transfer functions were trained and used to predict the LAI of forest stands.Results: The correlation coefficients between LAI and stand parameters(stand number of trees, basal area, the quadratic mean diameter, stand density and stand age) were significant at the level of 0.01. The stand age, number of trees, site index, and basal area were independent parameters in the most successful regression model predicted LAI values using stand parameters(R_(adj)~2=0.5431). As corresponding method to predict the interactions between the stand LAI values and stand parameters, the neural network architecture based on the RBF 4-19-1 with Gaussian activation function in hidden layer and the identity activation function in output layer performed better in predicting LAI(SSE(12.1040), MSE(0.1223), RMSE(0.3497), AIC(0.1040), BIC(-77.7310) and R^2(0.6392)) compared to the other studied techniques.Conclusion: The ANN outperformed the multivariate regression techniques in predicting LAI from stand parameters. The ANN models, developed in this study, may aid in making forest management planning in study forest stands.展开更多
文摘In this article, authors introduce a method to assess local influence of obser- vations on the parameter estimates and prediction in multivariate regression model. The diagnostics under the perturbations of error variance, response variables and explanatory variables are derived, and the results are compared with those of case- deletion. Two examples are analyzed for illustration.
基金supported by the Natural Sciences and Engineering Research Council of Canadathe National Natural Science Foundation of China+2 种基金the Doctorial Fund of Education Ministry of Chinasupported by the Natural Sciences and Engineering Research Council of Canadasupported by the National Natural Science Foundation of China
文摘Recursive algorithms are very useful for computing M-estimators of regression coefficients and scatter parameters. In this article, it is shown that for a nondecreasing ul （t）, under some mild conditions the recursive M-estimators of regression coefficients and scatter parameters are strongly consistent and the recursive M-estimator of the regression coefficients is also asymptotically normal distributed. Furthermore, optimal recursive M-estimators, asymptotic efficiencies of recursive M-estimators and asymptotic relative efficiencies between recursive M-estimators of regression coefficients are studied.
基金Funding from The Scientific and Technological Research Council of Turkey(Project No:2130026)is gratefully acknowledged
文摘Background: Leaf Area Index(LAI) is an important parameter used in monitoring and modeling of forest ecosystems. The aim of this study was to evaluate performance of the artificial neural network(ANN) models to predict the LAI by comparing the regression analysis models as the classical method in these pure and even-aged Crimean pine forest stands.Methods: One hundred eight temporary sample plots were collected from Crimean pine forest stands to estimate stand parameters. Each sample plot was imaged with hemispherical photographs to detect the LAI. The partial correlation analysis was used to assess the relationships between the stand LAI values and stand parameters, and the multivariate linear regression analysis was used to predict the LAI from stand parameters. Different artificial neural network models comprising different number of neuron and transfer functions were trained and used to predict the LAI of forest stands.Results: The correlation coefficients between LAI and stand parameters(stand number of trees, basal area, the quadratic mean diameter, stand density and stand age) were significant at the level of 0.01. The stand age, number of trees, site index, and basal area were independent parameters in the most successful regression model predicted LAI values using stand parameters(R_(adj)~2=0.5431). As corresponding method to predict the interactions between the stand LAI values and stand parameters, the neural network architecture based on the RBF 4-19-1 with Gaussian activation function in hidden layer and the identity activation function in output layer performed better in predicting LAI(SSE(12.1040), MSE(0.1223), RMSE(0.3497), AIC(0.1040), BIC(-77.7310) and R^2(0.6392)) compared to the other studied techniques.Conclusion: The ANN outperformed the multivariate regression techniques in predicting LAI from stand parameters. The ANN models, developed in this study, may aid in making forest management planning in study forest stands.
