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张东云 《经济数学》2013,(3):103-106
本文主要研究非参数异方差回归模型的局部多项式估计问题.首先利用局部线性逼近的技巧,得到了回归均值函数的局部极大似然估计.然后,考虑到回归方差函数的非负性,利用局部对数多项式拟合,得到了方差函数的局部多项式估计,保证了估计量的非负性,并证明了估计量的渐近性质.最后,通过对农村居民消费与收入的实证研究,说明了非参数异方差回归模型的局部多项式方法比普通最小二乘估计法的拟合效果更好,并且预测的精度更高.  相似文献
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We introduce a nonlinear regression modeling strategy, using a regularized local likelihood method. The local likelihood method is effective for analyzing data with complex structure. It might be, however, pointed out that the stability of the local likelihood estimator is not necessarily guaranteed in the case that the structure of system is quite complex. In order to overcome this difficulty, we propose a regularized local likelihood method with a polynomial function which unites local likelihood and regularization. A crucial issue in constructing nonlinear regression models is the choice of a smoothing parameter, the degree of polynomial and a regularization parameter. In order to evaluate models estimated by the regularized local likelihood method, we derive a model selection criterion from an information-theoretic point of view. Real data analysis and Monte Carlo experiments are conducted to examine the performance of our modeling strategy.  相似文献
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