An embedded and charset-unspecified text was scrubbed... Name: not available URL: <https://stat.ethz.ch/pipermail/r-help/attachments/20111019/f5a5e3a2/attachment.pl>
Estimating bivariate normal density with constrains
2 messages · Serguei Kaniovski, Rolf Turner
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