
variance of "roots of implicit function"
Posted:
Jul 23, 2012 7:16 AM


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.

