[转载] why median is less efficiency than mean? - 未名空间MITBBS历史存档

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[转载] why median is less efficiency than mean?

[转载] why median is less efficiency than mean?# Economics - 经济

n*s2003-04-09 07:04

1 楼

【以下文字转载自 Mathematics 讨论区,原文如下】
发信人: needreasons (walkman), 信区: Mathematics
标题: why median is less efficiency than mean?
发信站: The unknown SPACE (Wed Apr 9 18:27:51 2003) WWW-POST
I'm reading "Introduction to Robust and Quasi-Robust Statistical Methods" by
William J. J. Rey.
I page 5, it says " It is well known that estimation of the normal
distribution location by the median instead of the mean leads to an efficiency
loss of 36, ..."
Could anyone tell me why? Or recommend a book on how to ca

p*e2003-04-09 07:04

2 楼

Efficiency, in most case, only means min. variance for all linear
unbiased estimators. this is just the conclusion of the trivial
Gauss-Markov theorem, should be taught in any linear regression class;
or page 3 in any regression book.
If the errors are NORMAL, (like in your case), MLE will be the same as
LSE, it reaches the Rao-Cramer lower bound, (info. matrix)
how come you are reading robust estimators, while having
no clue of those basic results???????????
FTing......

efficiency
efficiency?

【在 n*********s 的大作中提到】

: 【以下文字转载自 Mathematics 讨论区,原文如下】
: 发信人: needreasons (walkman), 信区: Mathematics
: 标题: why median is less efficiency than mean?
: 发信站: The unknown SPACE (Wed Apr 9 18:27:51 2003) WWW-POST
: I'm reading "Introduction to Robust and Quasi-Robust Statistical Methods" by
: William J. J. Rey.
: I page 5, it says " It is well known that estimation of the normal
: distribution location by the median instead of the mean leads to an efficiency
: loss of 36, ..."
: Could anyone tell me why? Or recommend a book on how to ca