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We consider deterministic parameter estimation and 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 random variables as well. Unfortunately, in the general case, this marginalization is mathematically intractable, which prevents from using the known standard deterministic lower bounds (LBs) on the mean squared error (MSE). Actually the general case can be tackled by embedding the initial observation space in a hybrid one where any standard LB can be transformed into a modified one fitted to nonstandard deterministic estimation, at the expense of tightness however. Furthermore, these modified LBs (MLBs) appears to include the submatrix of hybrid LBs which is an LB for the deterministic parameters. Moreover, since in the nonstandard estimation, maximum likelihood estimators (MLEs) can be no longer derived, suboptimal nonstandard MLEs (NSMLEs) are proposed as being a substitute. We show that any standard LB on the MSE of MLEs has a nonstandard version lower bounding the MSE of NSMLEs. We provide an analysis of the relative performance of the NSMLEs, as well as a comparison with the MLBs for a large class of estimation problems. Last, the general approach introduced is exemplified, among other things, with a new look at the well-known Gaussian complex observation models. [ABSTRACT FROM PUBLISHER]

This letter investigates hybrid lower bounds on the mean square error in order to predict the so-called threshold effect. A new family of tighter hybrid large error bounds based on linear transformations (discrete or integral) of a mixture of the McAulay–Seidman bound and the Weiss–Weinstein bound is provided in multivariate parameters case with multiple test points. For use in applications, we give a closed-form expression of the proposed bound for a set of Gaussian observation models with parameterized mean, including tones estimation which exemplifies the threshold prediction capability of the proposed bound. [ABSTRACT FROM PUBLISHER]

Provided that one keeps in mind the Cram?er-Rao bound (CRB) limitations, that is, to become an overly optimistic lower bound when the observation conditions degrades, the CRB is a lower bound of great interest for analysis and design of a system of measurement in the asymptotic region. As a contribution, we introduce an original framework taking into account most (and possibly all) of the factors impacting the asymptotic estimation performance of the parameters of interest via equality constraints, leading to direct algebraic computations of constrained CRB. For complex systems, derivation of analytical expression of CRB is either impossible or inefficient. For application to active systems of measurement such as radar, we provide the general form of the Fisher information matrix (FIM) for multiple conditional models, which generally precludes the derivation of an analytical expression of the CRB for scenarios including interference and sensors modelling errors. We show that the proposed framework can also be used efficiently to generate new closed-form expressions of CRB, although this is not its main aim. [ABSTRACT FROM AUTHOR]