半参数平差模型参数的两步估计

Two-step estimation of parameters for semi-parametric adjustment models

考虑半参数平差模型L=Bx+S+Δ,xεRd,S为未知回归参数,为未知Borel函数。本文首先利用自然样条函数法,找到符合条件的非参数自然样条插值函数。其次利用偏残差法并综合最小二乘法,导出了参数和非参数的解算公式,讨论了窗宽参数的选取方法。在本文的最后,将这种估计方法应用到重力场的计算中,说明了利用半参数平差模型估计参数的有效性。

Considering the Semi-parametric adjustment models L=Bx+S+Δ,where,x∈Rdis a d-vector of unknown parameters,S is an unknown Borel function.In this paper,with natural cubic spline methods,the natural cubic spline function of nonparametric component Sis found firstly.THEN,the solving formula of parameters βand S are derived by using the partial residual and least square method.The selection of bandwidth is discussed too.Finally,this method is applied in the calculation of gravity.The result shows that it is effective.