Abstract: The condition appling the simple least squares estimator to parameter estimation without any loss of information, given by C. R. Rao in 1965, is difficult to satisfy in practice. In document [2] a kind of measure of information loss was given. This paper, by means of document [3], discusses another kind of measure of information loss and concludes that the result of docament [3] is a new kind of kan torovich inequality, and in the end, we give the inequality (14) that is more general than that of the document[3].

Key words: least squares estimator, linear model, robustness

摘要： 1965年,C.R.Rao给出了参数估计中运用简单最小二乘估计而不蒙受任何信息、损失的条件,见文[1],但在实际中它是很难满足的.文[2]给出了一种信息损失度量.本文借助于文[3]建议的一个结果,讨论了另一类信息损失度量,并指出了文[3]的结果实际上是一类新的Kantorovich不等式,最后本文建立了比文[3]的结果更一般的不等式(14).

关键词: 最小二乘估计, 线性模型, 稳健性