Lower bounds for non standard deterministic estimation

Galy, Jérôme; Chaumette, Éric; Vincent, François; Renaux, Alexandre; Larzabal, Pascal

doi:10.1109/sam.2016.7569710

Cited by 2 publications

(5 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Kbayer (1) , J. Galy (2) , E. Chaumette (3) , F. Vincent (3) , A. Renaux (4) and P. Larzabal (5) (1) Tésa/Isae-Supaero, Université de Toulouse, 7 Boulevard de la Gare, Toulouse, France (nabil.kbayer@isae.fr) (2) Université de Montpellier 2/LIRMM, 161 rue Ada, Montpellier, France (galy@lirmm.fr) (3) Isae-Supaero, Université de Toulouse, 10 av. Edouard Belin, Toulouse, France ([eric.chaumette, francois.vincent]@isae.fr) (4) Université Paris-Sud/LSS, 3 Rue Joliot-Curie, Gif-sur-Yvette, France (renaux@lss.supelec.fr) (5) Université Paris-Sud/SATIE, 61 av. du President Wilson, Cachan, France (pascal.larzabal@satie.ens-cachan.fr)…”

Section: Estimation Accuracy Of Non-standard Maximum Likelihood Estimunclassified

“…Since any existing standard Small-Error [7][15]- [18] or Large-Error bound [19]- [26][28]- [31] on φ can be obtained from (8c), it has a non-standard form obtained from E θr |θ C φ φ BBA [5]. Let us recall that in general φ BBA φ BBA (x; φ) ∈ U (∆), therefore the associated NSLB can not be compared a priori neither with the MSE of θML ∈ V (Ω) nor with any of its LBs (computed with p (x|θ)).…”

Section: Further Considerationsmentioning

confidence: 99%

“…However if p (θr|θ) does not depend on θ, then one can derive inequalities between modified [5] and nonstandard LBs (proofs are given in [36]). In the general case where p (θr|θ) does depend on θ, no general inequalities between modified and non-standard LBs can any longer be exhibited; comparisons are possible only on a "case-by-case basis".…”

Section: Further Considerationsmentioning

confidence: 99%

“…[4]. Therefore, as recalled in [5], deterministic estimation problems can be divided into two subsets: the subset of "standard" estimation problems for which a closed-form expression of p (x|θ) is available, and the subset of "non-standard" estimation problems for which only an integral form of p (x|θ) (1) is available. Since in non-standard estimation, maximum likelihood estimators (MLEs) (2a) can be no longer derived, the use of joint MLEs of θ and θr (2b) are proposed as being a substitute:…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Estimation accuracy of non-standard maximum likelihood estimators

Kbayer

Galy

Chaumette

et al. 2017

2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

View full text Add to dashboard Cite

In many deterministic estimation problems, 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, this marginalization is often mathematically intractable, which prevents from using standard maximum likelihood estimators (MLEs) or any standard lower bound on their mean squared error (MSE). To circumvent this problem, the use of joint MLEs of deterministic and random parameters are proposed as being a substitute. It is shown that, regarding the deterministic parameters: 1) the joint MLEs provide generally suboptimal estimates in any asymptotic regions of operation yielding unbiased efficient estimates, 2) any representative of the two general classes of lower bounds, respectively the Small-Error bounds and the Large-Error bounds, has a "non-standard" version lower bounding the MSE of the deterministic parameters estimate.

show abstract

Section: Estimation Accuracy Of Non-standard Maximum Likelihood Estimunclassified

Section: Further Considerationsmentioning

confidence: 99%

Section: Further Considerationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Estimation accuracy of non-standard maximum likelihood estimators

Kbayer

Galy

Chaumette

et al. 2017

2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

View full text Add to dashboard Cite

show abstract

“…As a first contribution sketchily disclosed in [43], a unified framework for the derivation of LBs on the MSE for unbiased estimates in non-standard estimation is more fully developed. The proposed framework exploits the fact that the MSE is the square of a norm defined on the vector space of square integrable functions θ (x) and, therefore, all known standard LBs on the MSE can be formulated as the solution of a norm minimization problem under linear constraints [20] [23] [25] [44].…”

Section: Introductionmentioning

confidence: 99%

On Lower Bounds for Nonstandard Deterministic Estimation

Kbayer¹,

Galy

Chaumette

et al. 2017

IEEE Trans. Signal Process.

Self Cite

View full text Add to dashboard Cite

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 an hybrid one where any standard LB can be transformed into a modified one fitted to non-standard deterministic estimation, at the expense of tightness however. Furthermore, these modified LBs (MLBs) appears to include the sub-matrix of hybrid lower bounds which is a LB for the deterministic parameters. Moreover, since in non-standard estimation, maximum likelihood estimators (MLEs) can be no longer derived, suboptimal non-standard MLEs (NSMLEs) are proposed as being a substitute. We show that any standard LB on the MSE of MLEs has a non-standard 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 modified LBs 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.

show abstract

Lower bounds for non standard deterministic estimation

Cited by 2 publications

References 35 publications

Estimation accuracy of non-standard maximum likelihood estimators

Estimation accuracy of non-standard maximum likelihood estimators

On Lower Bounds for Nonstandard Deterministic Estimation

Contact Info

Product

Resources

About