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Briefly, $h(\cdot)$ is a change of variable, and not a statistic. In the assumption of the $\delta$-method, we already have that $\hat{\theta}$ is scaled by $\sqrt{n}$ so that the limiting distribution has a finite, non-zero variance. As a corollary we can say $\text{Var}(\theta) \approx I_n(\theta)^{-1} / n$ for large $n$, and a similar statement can be ...


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Sort of not answering your question, but the brms R package covers the multinomial model. E.g. like this brm(bf(y | trials(size) ~ 1, muy2 ~ x), data = mydata, family = multinomial(), prior = myprior) (see e.g. here). The great thing - assuming you are happy with a Bayesian approach - is that you can then get predictions based on each MCMC sample. One of ...


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