1d:T6e3,# 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. ```r mle_weighted(mles) ``` ## Arguments - `mles`: A list of `mle` objects, all for the same parameter. ## Returns 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. ## Examples ```r # Combine three independent estimates of mean set.seed(123) # Three independent samples x1 <- rnorm(50, mean = 10, sd = 2) x2 <- rnorm(30, mean = 10, sd = 2) x3 <- rnorm(70, mean = 10, sd = 2) # Create MLE objects for each sample make_mean_mle <- function(x) { n <- length(x) s2 <- var(x) mle(theta.hat = mean(x), sigma = matrix(s2/n), info = matrix(n/s2), nobs = n) } fit1 <- make_mean_mle(x1) fit2 <- make_mean_mle(x2) fit3 <- make_mean_mle(x3) # Combine using inverse-variance weighting combined <- mle_weighted(list(fit1, fit2, fit3)) params(combined) se(combined) ```1e:T49a,M7.49933 0.25C3.49635 0.25 0.25 3.49593 0.25 7.50024C0.25 10.703 2.32715 13.4206 5.2081 14.3797C5.57084 14.446 5.70302 14.2222 5.70302 14.0299C5.70302 13.8576 5.69679 13.4019 5.69323 12.797C3.67661 13.235 3.25112 11.825 3.25112 11.825C2.92132 10.9874 2.44599 10.7644 2.

mle_weighted function