ON THE ESTIMATION OF DISPERSION BY LINEAR SYSTEMATIC STATISTICS
成果类型：
Article
署名作者：
GODWIN, HJ
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.1093/biomet/36.1-2.92
发表日期：
1949
页码：
92100
关键词：
摘要：
A linear systematic estimate of the standard deviation of a distribution, F(x), is a linear combination of the order statistics x1[less than or equal] X2 [less than or equal]...[less than or equal]Xn in a sample of n, and may be expressed in the form [image] where yi = Xi+1[long dash]Xi . First and 2d moments of the yi are expressed as linear combinations of [image]and [image]. It is shown that the efficiency of the linear systematic statistic, d, may always be maximized. Two applications are given. For the rectangular distribution, the sample range is most efficient, with the relative efficiency of the me.an deviation decreasing to zero as sample size increases to infinity. For normal distributions, the range is best for sample sizes up to 6; also the mean deviation from the median is less efficient than the mean deviation from the mean but the ratio of efficiencies is not less than 0.945. It also appears that, in the normal case, it should be possible to construct a much better linear statistic than any currently being used.