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Topic: aprroximation to function of a statistitics
Replies: 3   Last Post: Aug 14, 2012 12:40 PM

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Herman Rubin

Posts: 399
Registered: 2/4/10
Re: aprroximation to function of a statistitics
Posted: Aug 14, 2012 11:18 AM
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On 2012-08-14, oercim <> wrote:

> Hello I need help, I want to calculate variance of functional. Let
v1=var(x) > My aim is to calculate a function of x depending parameter "a":

> var(f(x,a)) where "a" is the parameter.

> To approximate this variance I used delta method. However in simulation
results for some values of "a" the approximation didn't work well possibly
heavy nonlinearity of g.

> I dont want to use resampling mathods(like bootstrap or jacknife). Is
there another ways to approximate the variance. Is higher order
approximation possible? I searched google but I could not find a
sufficient source. If you help me about this object, I will be very glad.

You might be able to expand the expression, but you will need more
than the variance to carry out the calculations.

One way to see if non-linearity is a problem is to check the
means in the simulation. This checks for quadratic terms,
but the means behaving is not a guarantee. Another possible
source of the observed problem is the pseudo-random numbers
being used; pseudo-random numbers are NOT random, and there
are ways around that problem by incorporating physical
random numbers.

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 Phone: (765)494-6054 FAX: (765)494-0558

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