Statistical functionals are called elicitable if there exists a loss or scoring function under which the functional is optimal point forecast in expectation. While mean and quantiles elicitable, it has been shown Heinrich (2014) that mode cannot be elicited true distribution can follow any Lebesgue density. We strengthen this result substantially, showing with continuous density unique local ma...

let $pounds$ be the category of locally compact abelian groups and $a,cin pounds$. in this paper, we define component extensions of $a$ by $c$ and show that the set of all component extensions of $a$ by $c$ forms a subgroup of $ext(c,a)$ whenever $a$ is a connected group. we establish conditions under which the component extensions split and determine lca groups which are component projective. ...