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半参数模型解算的补偿最小二乘法用于模型精化和系统误差分离的优良效果已被人们所共知。该法应用的难点在于正则矩阵和平滑参数的确定,就平滑参数的确定而言,一般需要通过特定方法在非负实数中选取,范围很大。本文提出一种等价补偿最小二乘准则,该准则尝试利用相对权比的方式保持残差项和补偿项之间的平衡关系。由于相对权比之和等于1,且分别在不大于1的正数中变化,故可将在非负实数中选取平滑参数的问题转换为在不大于1的正数中确定相对权比的问题。推导了该规则下解的形式和相关简单统计性质,模拟算例验证了新方法的可行性。
It is well known that the compensated least square method for solving the semiparametric model is good for model refinement and system error separation. The difficulty of applying this method lies in the determination of regular matrix and smoothing parameters. For the determination of smoothing parameters, it is generally required to select nonnegative real numbers by a specific method and have a large range. This paper presents an equivalent compensation least squares criterion, which attempts to maintain the balance between the residuals and the compensation terms by means of relative weighting. Since the sum of the relative weights is equal to 1 and each varies in positive numbers not larger than 1, the problem of selecting smoothing parameters in non-negative real numbers can be converted to the problem of determining the relative weighting ratios in positive numbers not larger than 1 . The form of the solution under the rule and the related simple statistical properties are deduced. Simulation results show the feasibility of the new method.