I am reading a book on Bayesian Estimation and Sensor Fusion and I want to know where the formula below come from. In fact, what is the relation between the variance and the second derivative of the ML estimation?
2026-03-29 18:01:50.1774807310
variance of a Maximum Liklihood estimator
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It is the variance of a weighted sum of independent RVs (in a slightly odd form)
If: $$ \hat{x}=\sum_{k=1}^n \alpha_k x_k $$
where the $X_k, k=1\dots n$ are independent RVs then:
$$ \mbox{Var}(\hat{X})=\sum_{k=1}^n \alpha_k^2 \mbox{Var}(X_k) $$
But: $\alpha_k=\frac{\partial \hat{x}}{\partial x_k}$