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 缺少精确先验时,不等式约束可改善参数估计。针对不等式约束M估计,利用巴哈杜尔线性化原理和凝聚函数方法导出参数估计、残差向量以及观测量平差量线性表达式,进一步导出相应的方差协方差矩阵和均方误差矩阵。线性表达式说明不等式约束M估计通常情况下是有偏的;均方误差矩阵公式表明不等式约束M估计解有可能改善,条件是最大不等式绝对值小于所导出的阈值,阈值由M估计的第一、第二多余参数和与不等式约束有关的多余参数确定。针对正态分布和p范分布确定了Lp估计改善解的具体条件。所导出的公式和结论可用于统计分析和不等式设计。 更多还原

【Abstract】 When lack of exact prior information,it is possible to use inequality constraints for improving solutions.To inequality constrained M-estimate(ICME),it is derived that the linear representations of the parameter estimator,residual vector and adjusted vector of observations by using Bahadur linearization principle and aggregate function method.The corresponding variance-covariance matrix(VCV) and the mean squares error matrix(MSE) are also obtained.The Bahadur linear representation shows that the... 更多还原