Accepts a list of `mle` objects for some parameter, say `theta`, and combines them into a single estimator `mle_weighted`.

It combines the `mle` objects by adding them together, weighted by the inverse of their respective variance-covariance matrix (information matrix). Intuitively, the higher the variance, the less weight an `mle` is given in the summation, or alternatively, the more information it has about the parameter, the more weight it is given in the summation.

Usage

mle_weighted(mles)

Arguments

mles

A list of `mle` objects, all for the same parameter.

Value

An object of type `mle_weighted` (which inherits from `mle`) that is the weighted sum of the `mle` objects.

Details

Each `mle` object should have an `observed_fim` method, which returns the Fisher information matrix (FIM) for the parameter. The FIM is assumed to be the negative of the expected value of the Hessian of the log-likelihood function. The `mle` objects should also have a `params` method, which returns the parameter vector.

We assume that the observations used to estimate each of the MLE objects in `mles` are independent.