补偿最小二乘模型的相对权比解法  

A new method for penalized least squares by weight scaling factor

作　　者：张俊[1,2] 独知行[1] 张显云[2] 

机构地区：[1]山东科技大学测绘科学与工程学院,山东青岛266510 [2]贵州大学矿业学院,贵阳550025

出　　处：《工程勘察》2013年第5期55-58,80,共5页Geotechnical Investigation & Surveying

基　　金：国家自然科学基金项目(41274006);教育部博士点基金项目(2010371810003);贵州大学青年自然科学基金项目(贵大自青基合字2009(077));贵州省自然科学基金项目(黔科合J字[2009]2264号)

摘　　要：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。The good effect that the semi-parametric model under the penalized least squares method for model refining and separation of systematic errors has been known to all. The difficulty of using the compensated least .squares is how to select the regular matrix and the smoothing parameter. On the smoothing parameter only, it is usually need to be selected in a large range of the nonnegative real numbers by some special methods. In this paper, a new method by attaching weight scaling factors both to the residual error quadries and systematic error quadric has been put forward to reduce the range of the smoothing parameters. The effect of the two weight scaling factors is still to maintain the balance between the residual error quadries and the non-parameter part. To ensure the balance, the sum of the two parameters is requested to be equal to 1, and the smoothing parameters scale must be between 0 and 1, which greatly reduces the smoothing parameter selection range. The simulated examples are demonstrated and some conclusions are drawn.

关 键 词：半参数模型 补偿最小二乘 平滑参数 相对权比 

分 类 号：TU196[建筑科学—建筑理论] P207[天文地球—测绘科学与技术]