半参数模型补偿最小二乘平滑参数求解新方法

New Method to Acquire Smoothing Parameter of Semi-Parametric Model Under Penalized Least Squares

半参数模型的补偿最小二乘法用于测量平差,是基于残差带权平方和与系统误差补偿项在极小化过程中的平衡关系而提出的,这种平衡是通过附加在补偿项的平滑参数来实现的。通常平滑参数需在非负实数中选择,无明确上界,范围过大,不利于平滑参数的确定。鉴于此,尝试对残差和补偿项赋予相对权比,以简化平滑参数的求解,并实现二者平衡关系的调节。由于相对权比在数值上小于1且其和等于1,故残差和补偿项的相对权比都具有明确的上下界,因此,可将在无明确上界的非负实数中寻求平滑参数的问题转化为在明确范围内确定相对权比的问题。给出了此种情况下的半参数模型的补偿解的表达式及简单统计性质,并用模拟算例验证了本法的可行性。

The semi-parametric model under the penalized least squares method for survey adjustment is based on the principle of balance between the weighted sum-squared residual errors and systematic errors.This balance is achieved by attaching a smoothing parameter to the penalized part.That is systematic errors part.Because large selecting scale of the smoothing parameter,selecting an appropriate smoothing parameter becomes a difficult and key problem.A method of semi-parametric model under the penalized least squares with weight scaling factor is put forward and the formula and statistical properties of estimates are deduced.To ensure the balance of the two parts,the sum of weight scaling factors of two parts must be equal to 1 and restricted between 0 and 1,greatly reduces the smoothing parameter selection range.The simulated examples are demonstrated and some conclusions are drawn.