赋双平滑参数的广义补偿最小二乘估计

The Method of Universal Penalized Least Squares by Adding Smoothing Parameters Both to the Residual and Systematic Parts

基于补偿最小二乘法思想,研究推导了半参数模型解算的极小化过程中,在残差和补偿项均赋予平滑参数的广义补偿最小二乘估计解的形式及其均方误差计算公式;模拟算例表明:在这种规则下,不仅可以克服病态性对半参数模型解的影响,而且也可以正确分离系统误差。新规则下,要求赋予的两个平滑参数之和等于1,各平滑参数严格限定在区间(0,1],从而使平滑参数的选择范围得到大幅缩小,为本法的应用提供了有利条件。

A new mothed that adding smoothing parameters both to the residual errors and systemic errors at the same time based on the principle of universal Penalized least squares is put forward and the solution formulation and the corresponding mean square errors are given. To ensure the balance of the residual errors and systemic errors, the sum of smoothing parameters of two parts are requested to be equal to 1, and the smoothing parameters scale must be restricted to between 0 and 1, which greatly reduces the selection range of smoothing parameter. A simulated example has been demonstrated and the results show that the new method can not only eliminate the effect of ill-condition but also can achieve satisfactory solutions of parameters and the systemic errors.