半参数回归与模型精化

Semiparametric Regression and Model Refining

就一般情况给出了半参数平差的算法 ,并结合一种特定的情况 ,讨论了正规化矩阵半正定时的计算方法 ,给出了相应的公式。最后构造了一个模拟的平差问题 ,对半参数法和最小二乘法的计算结果进行了比较。计算表明 。

When the functional model of a surveying adjustment problem contains model errors or the measurements inherit systematic errors,especially when this kind of errors can hardly be described by a few parameters,conventional adjustment method of least squares can not correctly identify this kind of errors which will affect estimations of the unknown parameters badly and sometimes even give a false conclusion.This paper solves this problem effectively by introducing the semiparametric estimate model into surveying adjustment theory.Actually the semiparametric model is the conventional G_M linear model adding a nonparametric.Because there are more unknown parameters being added,the method of least squares can not provide a unique solution.This paper presents a semiparametric adjustment method fit for the general case.The calculation method is discussed and the corresponding formulas are presented.Finally,a simulated adjustment problem is constructed to explain the method.The results of the semiparametric model and G_M model are compared,which demonstrates that the model errors or the systematic errors of the observations can be detected correctly by the semiparametric estimate method.