On 20/10/11 02:31, Serguei Kaniovski wrote:
Dear R-Users
I would like to estimate a constrained bivariate normal density, the
constraint being that the means are of equal magnitude but of opposite
signs. So I need to estimate four parameters:
mu (meanvector (mu,-mu))
sigma_1 and sigma_2 (two sd deviations)
rho (correlation coefficient)
I have looked at several packages, including Gaussian mixture models in
Mclust, but I am not sure what is the best way, or the best package to use
for this task.
Greatly appreciate any suggestions!
I very much doubt that there is anything built-in that you can use.
However it shouldn't be *too* hard to get maximum likelihood estimates
using optim() to maximise the (log) likelihood.
For starting values I would try just using the ordinary covariance
matrix estimate to get your sigma_1, sigma_2, and rho estimates,
and for mu use (x1.bar - x2.bar)/2 (in what I hope is an obvious
notation) for a starting value.
Good luck!
cheers,
Rolf Turner
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