回归模型误差补偿半参数法中正则矩阵任意时的参数估计  

Parameter estimation on random regular matrix in regression model error compensation semi parametric method

作　　者：张志伟[1] 胡伍生[1] 黄晓明[1] 

机构地区：[1]东南大学交通学院,南京210096

出　　处：《测绘科学》2011年第1期164-166,共3页Science of Surveying and Mapping

基　　金：国家863计划项目"空间数据挖掘的神经网络技术研究"(2007AA12Z228)

摘　　要：用试验观测数据建立的回归拟合模型不可避免地存在模型误差,将模型误差视为非参数分量列入回归模型的半参数模型是一种重要的回归模型。本文利用补偿最小二乘原理,导出了顾及预测点的半参数回归模型参数及模型误差的估计量,并对估计量进行精度评定,给出了估计量及精度评定的相应公式。在理论分析的基础上,得出了只要正则矩阵R的选取使法方程系数矩阵可逆,且rank(RA)=t,则参数和模型误差仍然有惟一解的结论。通过几个实例验证了结论的正确性和较强的稳定性,且模型效果更佳。为半参数回归模型参数估计时正则矩阵的选择提供了一种新的思路。The regression fitting model established with the experiment observation data inevitably has the model error. The model error as a non-parametric component included the semi parametric model of regression model is a significant regression model. The use of penalized least squares principle was taken into consideration of the predicted point to derive the semi parametric regression model parameter and the model error＇s estimator in the paper, and the precision evaluation was carried out to the estimator to give the estimator and the precision evaluation corresponding formula. In the basis of theoretical analysis, it obtained the conclusion that the parameter and the model error still had unique solution so long as the regular matrix R selection causes the normal equation coefficient matrix to be reversible and rank（BA） = t. The correctness and the strong stability of the conclusion were confirmed through several examples and the model effect was better. The conclusion provided a referencial way of thinking for the choice of regular matrix in semi parametric re- gression model parameter estimation.

关 键 词：回归模型 模型误差补偿 半参数 正则矩阵 参数估计 

分 类 号：P207[天文地球—测绘科学与技术]