a fundamental question about statistics
Jun. 1st, 2008 03:59 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
guslIf you have the MLEs for all the parameters that describe the family of distributions under consideration, is it always the case that you can trivially combine them into the MLE of the distribution?
e.g.: Gaussians are parametrized by mean and variance, and the MLE Gaussian is the one with the MLE mean as its mean, and the MLE variance as its variance.
If the two parameters are independent, in the sense that likelihood(p1, p2) = likelihood(p1) likelihood(p2), then the hypothesis follows.
e.g.: Gaussians are parametrized by mean and variance, and the MLE Gaussian is the one with the MLE mean as its mean, and the MLE variance as its variance.
If the two parameters are independent, in the sense that likelihood(p1, p2) = likelihood(p1) likelihood(p2), then the hypothesis follows.