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Science Forum Index » Statistics - Math Forum » Question about moments estimation
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| Bill August |
 Posted: Thu May 01, 2008 6:25 am |
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Hi All,
My problem is:
Y = g( f(X1, X2, X3, ...) ), Xn are random variables and f, g are functions.
Suppose I know the moments of f. The question is if it is possible to obtain the moments of Y?
Many thx. |
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| Herman Rubin |
| Posted: Thu May 01, 2008 1:05 pm |
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In article <8233296.1209659143513.JavaMail.jakarta@nitrogen.mathforum.org>,
Bill August <hui.song@beds.ac.uk> wrote:
Quote: Hi All,
My problem is:
Y = g( f(X1, X2, X3, ...) ), Xn are random variables and f, g are functions.
Suppose I know the moments of f. The question is if it is possible to obtain the moments of Y?
Many thx.
Under certain conditions, yes. If g is a polynomial
of finite degree, the answer is yes. If g is a
sufficiently rapidly converging power series, likewise.
Otherwise, the moments of f would have to determine
the distribution of f, and this is iffy. Necessary
and sufficient conditions are known, and the easist
version is that if one takes the regresson of 1 and
f on f^2, f^3, ..., the covariance matrix of the
residuals is singular. This condition is difficult,
and there are sufficient conditions, Generating a
distribution from its moments, if there is not a
good example in the literature is generally very
difficult.
If only a finite number of moments are available,
on can gat bounds for the moments of g, but they
are not likely to be very good.
--
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@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 |
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