中文摘要：

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。

英文摘要：

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 ICME is biased.The MSE matrix shows the possibility that the solutions are improved,and the condition of the improved solutions is that the maximum of the absolute inequality is smaller the derived threshold that is determined by the first and second nuisances of M-estimate and the nuisance associated with the inequality constraint;To the least p-norm estimate in the case of Gauss distribution and p-norm distribution,the clear improvement conditions are given out.The derived formula and conclusions can be used for statistical analysis and inequality design.