文章以幂函数变换为研究对象,从背景值误差和还原误差的角度分析了幂函数变换对GM(1,1)模型建模精度的影响,论证了幂函数变换的GM(1,1)模型(PFNGM(1,1)模型)具有逼近无偏性,能在可忽略的误差范围内实现对白指数序列的预测无偏性。实例...文章以幂函数变换为研究对象,从背景值误差和还原误差的角度分析了幂函数变换对GM(1,1)模型建模精度的影响,论证了幂函数变换的GM(1,1)模型(PFNGM(1,1)模型)具有逼近无偏性,能在可忽略的误差范围内实现对白指数序列的预测无偏性。实例应用结果表明,其建模精度和预测效果均优于无偏GM(1,1)模型和离散GM(1,1)模型。为将适宜建模序列拓展至近似非齐次指数序列和季节波动序列,同时保留幂函数变换可以有效降低背景值误差对建模精度影响的优势,将幂函数变换与平移变换相结合构建了PFNGM(1,1)模型,将幂函数变换与季节性GM(1,1)模型(SGM(1,1)模型)相结合构建了PFSGM(1,1)模型。实例应用结果表明,PFNGM(1,1)模型的建模精度和预测效果均优于背景值改进的NGM(1,1, k )模型和ONGM(1,1, k,c )模型,PFSGM(1,1)模型的建模精度和预测效果均优于SGM(1,1)模型,验证了两种模型的有效性。展开更多
In the seemingly unrelated regression systems, the existing quasi-likelihood is always involved in the difficult problem of calculating inverse of a high order matrix specially for large systems. To avoid this problem...In the seemingly unrelated regression systems, the existing quasi-likelihood is always involved in the difficult problem of calculating inverse of a high order matrix specially for large systems. To avoid this problem, the new quasi-likelihood proposed in this paper is based mainly on a linearly iterative process of some unbiased estimating functions.Some finite sample properties and asymptotic behaviours for this new quasi-likelihood are investigated. These results show that the new quasi-likelihood for parameter of interest is E-sufficient, iteratively efficient and approximately efficient. Some examples are given to illustrate the theoretical results.展开更多
文摘文章以幂函数变换为研究对象,从背景值误差和还原误差的角度分析了幂函数变换对GM(1,1)模型建模精度的影响,论证了幂函数变换的GM(1,1)模型(PFNGM(1,1)模型)具有逼近无偏性,能在可忽略的误差范围内实现对白指数序列的预测无偏性。实例应用结果表明,其建模精度和预测效果均优于无偏GM(1,1)模型和离散GM(1,1)模型。为将适宜建模序列拓展至近似非齐次指数序列和季节波动序列,同时保留幂函数变换可以有效降低背景值误差对建模精度影响的优势,将幂函数变换与平移变换相结合构建了PFNGM(1,1)模型,将幂函数变换与季节性GM(1,1)模型(SGM(1,1)模型)相结合构建了PFSGM(1,1)模型。实例应用结果表明,PFNGM(1,1)模型的建模精度和预测效果均优于背景值改进的NGM(1,1, k )模型和ONGM(1,1, k,c )模型,PFSGM(1,1)模型的建模精度和预测效果均优于SGM(1,1)模型,验证了两种模型的有效性。
基金Project supported by the National Natural Science Foundation of China (No.10371059, No.10171051).
文摘In the seemingly unrelated regression systems, the existing quasi-likelihood is always involved in the difficult problem of calculating inverse of a high order matrix specially for large systems. To avoid this problem, the new quasi-likelihood proposed in this paper is based mainly on a linearly iterative process of some unbiased estimating functions.Some finite sample properties and asymptotic behaviours for this new quasi-likelihood are investigated. These results show that the new quasi-likelihood for parameter of interest is E-sufficient, iteratively efficient and approximately efficient. Some examples are given to illustrate the theoretical results.
