Lower bounds for non standard deterministic estimation
Jérôme Galy, Éric Chaumette, François Vincent, Alexandre Renaux, Pascal Larzabal · 2016
In this paper, non standard deterministic parameters estimation is considered, i.e. the situation where the probability density function (p.d.f.) parameterized by unknown deterministic parameters results from the marginalization of a joint p.d.f. depending on additional random variables. Unfortunately, in the general case, this marginalization is mathematically intractable, which prevents from using the known deterministic lower bounds on the mean-squared-error (MSE). However an embedding mechanism allows to transpose all the known lowers bounds into modified lower bounds fitted with non-standard deterministic estimation, encompassing the modified Cramér-Rao/Bhattacharyya bounds and hybrid lower bounds.