补偿最小二乘半参数模型解及估计量的统计性质  

SOLUTION OF SEMIPARAMETRIC MODEL WITH DERAILIZED LEAST SQUARE AND STATISTIC CHARACTERISTICS OF ESTIMATOR

作　　者：丁士俊[1,2] 姜卫平[3] 

机构地区：[1]武汉大学测绘学院,武汉430079 [2]国家测绘局精密工程测量与工业测量重点实验室,武汉430079 [3]武汉大学卫星导航定位系统技术研究中心,武汉430079

出　　处：《大地测量与地球动力学》2010年第6期47-50,56,共5页Journal of Geodesy and Geodynamics

基　　金：国家自然科学基金(40604001);国家863计划项目(2007AA12Z312)

摘　　要：讨论半参数模型的两种不同求解方法,并导出相应解的计算公式与精度评定公式。另外从偶然误差的特性出发,研究半参数模型估计量的有偏性、估计量的分布以及参数估计的均方误差等统计性质。模拟实验表明,在半参数模型补偿最小二乘估计中,只有在一定的准则下正确选择参数,才能得到参数、非参数与方差因子的最佳估计值。The semiparametric model is a combination of classical linear model and nonparametric regression model.The two didfferent computing methods on the resolution of the semiparametric model under the principle of penalized least squares are discussed and the computation formulas of the resolutions and estimate accuracy are detailed.On the basis of the statistic characteristics of random error,the statistic characteristics of the semiparametric model estimators are discussed about mathematical expection,variances of estimates and mean square error of the parameter estimate.Finally,a simulated example is demonstrated and some conclusions are drawn.

关 键 词：半参数模型 非参数模型 补偿最小二乘 统计性质 偶然误差 

分 类 号：P207[天文地球—测绘科学与技术]