Estimating parameters from multivariate normal

jimmy1

I need to estimate parameters from data that follow a mutinormal distribution. The parameters that I need to estimate are contained in the expression for the mean of the marginal normal distributions. That is each marginal distribution has mean:

[tex] \frac{p_1*c_i + p_1*y}{p_1+p_2}[/tex]

where [tex]p_1[/tex], [tex]p_2[/tex] and [tex]y[/tex] are the paramters that I need to estimate and [tex]c_i[/tex] is just a known contant associated with the ith marginal. [tex]p_1[/tex] and [tex]p_2[/tex] are random parameters and [tex]y[/tex] is a fixed parameter.

I've tried using a multinormal likelihood approach, which gives an estimate for the mean as the sample mean, but how do I get estimate of the actual parameters from this sample mean? Can I even use this approach?

Also is there an added complexity to estimating parameters when there are random parameters, as is the case with [tex]p_1[/tex] and [tex]p_2[/tex]?

Any help, on how best to estimate the paramters [tex]p_1[/tex], [tex]p_2[/tex] and [tex]y[/tex] would be great?