Re: sufficient statistics
- From: hrubin@xxxxxxxxxxxxxxxxxxxx (Herman Rubin)
- Date: 28 Nov 2006 12:39:47 -0500
In article <1164562079.333830.164350@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Kaushik <standshik@xxxxxxxxx> wrote:
hi all, i was just wondering if somebody could help me with this. i
want to know if there is some known result for the following problem.
let f(x|t) be a parametric probablity density function where the
parameter is t. let T(x) be (minimal) sufficient statictics. now if we
take expectation of T(x) with respect to t, i.e. E[T(x)] is there any
know result for the quantity | T(x)-E[T(x)] |? either upper bound lower
bound or some other relation? thanks
ps: i'm particularly interested in exponential families. if there is no
such result, is it possible to derive such a result for say,
exponential families?
There are lots of complete minimal sufficient statistics;
any 1-1 function of one is another. So the expectation
and variance are meaningless without specifying which one.
For exponential families, there is a "natural" sufficient
statistic, or for multivariate families, the appropriate
multivariate statistics. Their means and variances and
covariances can be computed from the normalizing function.
--
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
.
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- sufficient statistics
- From: Kaushik
- sufficient statistics
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