| 1. |
- Abdalmoaty, Mohamed, 1986-, et al.
(författare)
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Identification of Stochastic Nonlinear Models Using Optimal Estimating Functions
- 2020
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Ingår i: Automatica. - : Elsevier. - 0005-1098 .- 1873-2836. ; 119
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Tidskriftsartikel (refereegranskat)abstract
- The first part of the paper examines the asymptotic properties of linear prediction error method estimators, which were recently suggested for the identification of nonlinear stochastic dynamical models. It is shown that their accuracy depends not only on the shape of the unknown distribution of the data, but also on how the model is parameterized. Therefore, it is not obvious in general which linear prediction error method should be preferred. In the second part, the estimating functions approach is introduced and used to construct estimators that are asymptotically optimal with respect to a specific class of estimators. These estimators rely on a partial probabilistic parametric models, and therefore neither require the computations of the likelihood function nor any marginalization integrals. The convergence and consistency of the proposed estimators are established under standard regularity and identifiability assumptions akin to those of prediction error methods. The paper is concluded by several numerical simulation examples.
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| 2. |
- Abdalmoaty, Mohamed, 1986-, et al.
(författare)
-
The Gaussian MLE versus the Optimally weighted LSE
- 2020
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Ingår i: IEEE signal processing magazine (Print). - : Institute of Electrical and Electronics Engineers (IEEE). - 1053-5888 .- 1558-0792. ; 37:6, s. 195-199
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Tidskriftsartikel (refereegranskat)abstract
- In this note, we derive and compare the asymptotic covariance matrices of two parametric estimators: the Gaussian Maximum Likelihood Estimator (MLE), and the optimally weighted Least-Squares Estimator (LSE). We assume a general model parameterization where the model's mean and variance are jointly parameterized, and consider Gaussian and non-Gaussian data distributions.
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| 3. |
- Rodrigues, Diogo, et al.
(författare)
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Toward tractable global solutions to bayesian point estimation problems via sparse sum-of-squares relaxations
- 2020
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Ingår i: Proceedings American Control Conference, ACC 2020. - : Institute of Electrical and Electronics Engineers (IEEE). - 9781538682661 - 9781538682654 - 9781538682678 ; , s. 1501-1506
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Konferensbidrag (refereegranskat)abstract
- Bayesian point estimation is commonly used for system identification owing to its good properties for small sample sizes. Although this type of estimator is usually non-parametric, Bayes estimates can also be obtained for rational parametric models, which is often of interest. However, as in maximum-likelihood methods, the Bayes estimate is typically computed via local numerical optimization that requires good initialization and cannot guarantee global optimality. In this contribution, we propose a computationally tractable method that computes the Bayesian parameter estimates with posterior certification of global optimality via sum-of-squares polynomials and sparse semidefinite relaxations. It is shown that the method is applicable to certain discrete-time linear models, which takes advantage of the rational structure of these models and the sparsity in the Bayesian parameter estimation problem. The method is illustrated on a simulation model of a resonant system that is difficult to handle when the sample size is small.
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