Re: Sufficient Statistics
- From: hrubin@xxxxxxxxxxxxxxxxxxxx (Herman Rubin)
- Date: 2 Jan 2008 12:26:24 -0500
In article <61503fe0-cbcc-4483-be06-ab52e9115f61@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Yue <dariahuangster@xxxxxxxxx> wrote:
Dear all,
I was just reading some theoretical statistics notes and found a
sentence which puzzles me:
"
the entire data is always sufficient, so we need minimal sufficiency.
Do anyone know the explanation of the first part please?
thanks very much!
Suppose one has a statistical problem, with data D and a
probability model with states of nature W. Then a function
of the data S (it may be multidimensional) is sufficient
if any inference done from the full data can be matched for
all states of nature simultaneously by using the statistic.
This is NOT the usual definition, which gives easier ways
to verify sufficiency.
Examples are the sample mean and variance for normal
distributions, and the arithmetic and geometric means
for Gamma distributions. The set of likelihood rations
is always a minimal sufficient statistic; it is not
always convenient.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@xxxxxxxxxxxxxxx Phone: (765)494-6054 FAX: (765)494-0558
.
- References:
- Sufficient Statistics
- From: Yue
- Sufficient Statistics
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