带约束的参数平差函数模型的影响分析

来源期刊：中南大学学报(自然科学版)1997年第5期

论文作者：王志忠

文章页码：19 - 22

关键词：影响分析； Cook 距离； 最小二乘估计

Key words：influence analysis； Cook distance； least squares estimate

摘    要：为了适应测量数据处理理论的需要,本文概括了平差模型影响分析的主要成果,对CM模型数据扰动的影响分析方法进行了理论性的扩展,研究了带约束参数平差模型数据扰动的影响分析问题,建立了X_B(i)和X_B的关系式,其中X_B(i)表示删除约束模型第i组数据的最小二乘估计,X_B表示约束模型未知参数X的最小二乘估计。本文还研究了删除模型的统计性质,建立了度量扰动影的Cook距离。

Abstract: On the basis of the main results of influence analysis in the adjustment model and following the features and requirments of surveying data-processing, the influence analysis theory of the GM model is developed and the adjustment functional model under the restricted condition is studied. The paper establishes the relationship between X_B(i) and X_B, where X_B(i) denotes the least squares estimator of unknown parameter vector X of deleting the ith row of the adjustment model under the restricted condition and X_B denotes the least squared estimator of X in the adjustment model under the restricted condition. Cook distance, its functional properties and mathematical meaning are studied in detail.