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Topic: variance of "roots of implicit function"
Replies: 4   Last Post: Jul 26, 2012 6:46 PM

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Posts: 237
Registered: 5/2/05
variance of "roots of implicit function"
Posted: Jul 23, 2012 7:16 AM
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Hello. I have a problem. Let "a" be an unknown parameter, "x" be a random vector, and let "var" defines variance.

-Let g(x,a) is a random variable which is a function of parameter "a" and and also a function of random vector x. For each different random vector, g(x,a) takes different value. So g is also a random variable.

-I am interestested with the roots of g(x,a)=0 where g is an implicit function of "a". So roots will also be a random variable.

-Let: var(g(x,a))=f(a) where a is a known function of "a".

I want to find variance of the roots. Namely how can I find var(root(g(x,a)).
If you help me, or advice me sources, I will be very glad. Thanks alot.

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