On linear estimates with nearly minimum variance
On linear estimates with nearly minimum variance
复制标题
方差接近最小的线性估计
DOI：
--
复制
发表时间：
1957
期刊：
影响因子：
--
通讯作者：
G. Blom
中科院分区：
文献类型：
--
作者：
G. Blom
/~和a(Lloyd，1952)。这些估计可以被称为最佳无偏估计。该解的一个严重缺陷是，在大多数情况下，它涉及非常耗时的数值计算。本文的目的是证明，在一般条件下，可以找到一个方便的逼近最优解的方法，使之成为一个几乎最好的无偏估计。如一些例子所示，这种估计式的方差通常比最小方差高出很少。该方法的前提是变量x~的均值(但不是协方差)已知。对方法稍作修改，在均值和协方差都不知道的情况下也可以使用。由此产生的估计将被称为近乎最佳、近乎公正的估计。上面提到的两种类型的估计都是从下一节给出的一个定理推导出来的。
of /~ and a respectively (Lloyd, 1952). These est imates may be called best unbiased estimates. A serious drawback of the solution is tha t in most cases it involves very time-consuming numerical calculations. The object of this paper is to show that , under general conditions, it is possible to find a convenient approximation to the best solution which m a y be te rmed a nearly best unbiased estimate. The variance of this est imate is, as some examples will show, often very little in excess of the minimum variance. The method presupposes tha t t h e means (but not the covariances) of the variables x~ are known. By a slight modification of the method it may be used also when neither the means nor the covariances are known. The resulting estimates will be called nearly best, nearly unbiased estimates. Both types of estimates mentioned above m a y be derived from a theorem given in the next section.