MLE of Truncated Bivariate Normal
Suppose i have a dataset where each point comes from a truncated bivariate normal distribution say (u1,u2,sigma1,sigma2,pho) - all unknown. How do i find out the MLE (Maximum likelyhood Estimates) of the parameter??
If it is simple bivariate normal i can find it.
But what to do with the trucation term i.e. in the denomiator?
Let BV(mu,sigma) denotes the density (non truncated)
then the likelyhood function is BV(mu,sigma)/(integrate a to 100, 0 to 100) BV(mu,sigma)
which is a double integration in the denominator.
We need to take Log and then differentiate .. but im not getting a closed form of the denominator becos it contains the unknown terms.
Any help on how i can solve this???