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M C Campi - One of the best experts on this subject based on the ideXlab platform.
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non asymptotic confidence regions for the least squares Estimate
IFAC Proceedings Volumes, 2012Co-Authors: Balazs Csanad Csaji, M C Campi, Erik WeyerAbstract:Abstract We propose a new finite sample system identification method, called Sign-Perturbed Sums (SPS), to Estimate the parameters of dynamical systems under mild statistical assumptions. The proposed method constructs non-asymptotic confidence regions that include the Least-Squares (LS) Estimate and are guaranteed to contain the true parameters with a user-chosen exact probability. Our method builds on ideas imported from the “Leave-out Sign-dominant Correlation Regions” (LSCR) approach, but, unlike LSCR, also guarantees the inclusion of the LS Estimate and provides confidence regions for multiple parameters with exact probabilities. This paper presents the SPS method for FIR and ARX systems together with its main theoretical properties, as well as demonstrates the approach through simple examples and experiments.
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brief non asymptotic confidence ellipsoids for the least squares Estimate
Automatica, 2002Co-Authors: Erik Weyer, M C CampiAbstract:In this paper, we consider the finite sample properties of Least-Squares system identification, and derive non-asymptotic confidence ellipsoids for the Estimate. The shape of the confidence ellipsoids is similar to the shape of the ellipsoids derived using asymptotic theory, but unlike asymptotic theory, they are valid for a finite number of data points. The probability that the Estimate belongs to a certain ellipsoid has a natural dependence on the volume of the ellipsoid, the data generating mechanism, the model order and the number of data points available.
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non asymptotic quality assessment of the least squares Estimate
IFAC Proceedings Volumes, 2002Co-Authors: Su Ki Ooi, M C Campi, Erik WeyerAbstract:Abstract In any real-life identification problems, only a finite number of data points are available. On the other hand, almost all results in stochastic identification pertain to asymptotic properties, that is they tell us what happens when the number of data points tend to infinity. In this paper, we consider the problem of assessing the quality of non-asymptotic Estimates obtained using least squares identification methods. The type of results needed in order to be useful for computing the quality of non-asymptotic Estimates are first discussed. It turns out that the nature of non-asymptotic results has to be different from that of asymptotic results, since in finite time certain issues show up that disappear in the limit because of stochastic convergence. Then, we develop a method for the assessment of the Estimate quality based on differences between partial Estimates. If the partial Estimate differences are within a small region around zero then, as it is intuitive, the Estimate quality is good. On the other hand, we will have low confidence in the Estimate if the differences between partial Estimates are spread all over the place. The method is illustrated through a very simple example able to point out its main aspects in a clear-cut way.
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non asymptotic confidence ellipsoids for the least squares Estimate
Conference on Decision and Control, 2000Co-Authors: Erik Weyer, M C CampiAbstract:In this paper we consider the finite sample properties of least squares system identification, and we derive nonasymptotic confidence ellipsoids for the Estimate. Unlike asymptotic theory, the obtained confidence ellipsoids are valid for a finite number of data points. The probability that the Estimate belongs to a certain ellipsoid has a natural dependence on the volume of the ellipsoid, the data generating mechanism, the model order and the number of data points available.
Erik Weyer - One of the best experts on this subject based on the ideXlab platform.
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non asymptotic confidence regions for the least squares Estimate
IFAC Proceedings Volumes, 2012Co-Authors: Balazs Csanad Csaji, M C Campi, Erik WeyerAbstract:Abstract We propose a new finite sample system identification method, called Sign-Perturbed Sums (SPS), to Estimate the parameters of dynamical systems under mild statistical assumptions. The proposed method constructs non-asymptotic confidence regions that include the Least-Squares (LS) Estimate and are guaranteed to contain the true parameters with a user-chosen exact probability. Our method builds on ideas imported from the “Leave-out Sign-dominant Correlation Regions” (LSCR) approach, but, unlike LSCR, also guarantees the inclusion of the LS Estimate and provides confidence regions for multiple parameters with exact probabilities. This paper presents the SPS method for FIR and ARX systems together with its main theoretical properties, as well as demonstrates the approach through simple examples and experiments.
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brief non asymptotic confidence ellipsoids for the least squares Estimate
Automatica, 2002Co-Authors: Erik Weyer, M C CampiAbstract:In this paper, we consider the finite sample properties of Least-Squares system identification, and derive non-asymptotic confidence ellipsoids for the Estimate. The shape of the confidence ellipsoids is similar to the shape of the ellipsoids derived using asymptotic theory, but unlike asymptotic theory, they are valid for a finite number of data points. The probability that the Estimate belongs to a certain ellipsoid has a natural dependence on the volume of the ellipsoid, the data generating mechanism, the model order and the number of data points available.
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non asymptotic quality assessment of the least squares Estimate
IFAC Proceedings Volumes, 2002Co-Authors: Su Ki Ooi, M C Campi, Erik WeyerAbstract:Abstract In any real-life identification problems, only a finite number of data points are available. On the other hand, almost all results in stochastic identification pertain to asymptotic properties, that is they tell us what happens when the number of data points tend to infinity. In this paper, we consider the problem of assessing the quality of non-asymptotic Estimates obtained using least squares identification methods. The type of results needed in order to be useful for computing the quality of non-asymptotic Estimates are first discussed. It turns out that the nature of non-asymptotic results has to be different from that of asymptotic results, since in finite time certain issues show up that disappear in the limit because of stochastic convergence. Then, we develop a method for the assessment of the Estimate quality based on differences between partial Estimates. If the partial Estimate differences are within a small region around zero then, as it is intuitive, the Estimate quality is good. On the other hand, we will have low confidence in the Estimate if the differences between partial Estimates are spread all over the place. The method is illustrated through a very simple example able to point out its main aspects in a clear-cut way.
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non asymptotic confidence ellipsoids for the least squares Estimate
Conference on Decision and Control, 2000Co-Authors: Erik Weyer, M C CampiAbstract:In this paper we consider the finite sample properties of least squares system identification, and we derive nonasymptotic confidence ellipsoids for the Estimate. Unlike asymptotic theory, the obtained confidence ellipsoids are valid for a finite number of data points. The probability that the Estimate belongs to a certain ellipsoid has a natural dependence on the volume of the ellipsoid, the data generating mechanism, the model order and the number of data points available.
Torsten Soderstrom - One of the best experts on this subject based on the ideXlab platform.
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using boundary conditions for estimation of complex modulus from flexural wave experiments
IEEE Transactions on Control Systems and Technology, 2005Co-Authors: Kaushik Mahata, Saed Mousavi, Torsten Soderstrom, U ValdekAbstract:Estimation of the complex Young's modulus from transverse wave experiment is considered in this brief. The main goal is to modify the usual least squares Estimate so that additional information provided by the boundary conditions can be incorporated in the estimation algorithm. As a result, it is required to solve a constrained nonlinear least squares problem instead of an unconstrained one. The analytical results are validated using experimental data, where the modified Estimates outperform the conventional nonlinear least squares Estimate by a significant margin.
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on the use of flexural wave propagation experiments for identification of complex modulus
IEEE Transactions on Control Systems and Technology, 2003Co-Authors: Kaushik Mahata, Saed Mousavi, Torsten Soderstrom, Magnus Mossberg, U Valdek, L HillstromAbstract:In this paper, we investigate the nonparametric estimation of the frequency dependent complex modulus of a viscoelastic material. The strains due to flexural wave propagation in a bar specimen are registered at different cross sections. The time domain data is transformed into frequency domain using discrete Fourier transform and a nonlinear least squares algorithm is then employed to Estimate the complex modulus at each frequency. Inherent numerical problems due to associated ill-conditioned matrices are treated with special care. An analysis of the quality of the nonlinear least squares Estimate is also carried out. The validity of the theoretical results are confirmed by numerical studies and experimental tests.
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least squares parameter estimation of continuous time arx models from discrete time data
IEEE Transactions on Automatic Control, 1997Co-Authors: Torsten Soderstrom, Bengt Carlsson, S BigiAbstract:When modeling a system from discrete-time data, a continuous-time parameterization is desirable in some situations, In a direct estimation approach, the derivatives are approximated by appropriate differences. For an ARX model this lead to a linear regression. The well-known least squares method would then be very desirable since it can have good numerical properties and low computational burden, in particular for fast or nonuniform sampling. It is examined under what conditions a least squares fit for this linear regression will give adequate results for an ARX model. The choice of derivative approximation is crucial for this approach to be useful. Standard approximations like Euler backward or Euler forward cannot be used directly. The precise conditions on the derivative approximation are derived and analyzed. It is shown that if the highest order derivative is selected with care, a least squares Estimate will be accurate. The theoretical analysis is complemented by some numerical examples which provide further insight into the choice of derivative approximation.
Wei Xing Zheng - One of the best experts on this subject based on the ideXlab platform.
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space time semi blind equalizer for dispersive qam mimo system based on modified newton method
IEEE Transactions on Wireless Communications, 2014Co-Authors: Dazheng Feng, Wei Xing ZhengAbstract:This paper proposes a space-time semi-blind equalizer (ST-SBE) for dispersive multiple-input multiple-output (MIMO) communication systems that employ high throughput quadrature amplitude modulation (QAM) signals. A novel cost function (CF) that integrates multimodulus algorithm (MMA) with soft decision-directed (SDD) scheme is established to efficiently obtain the weight vector associated with the ST-SBE. In the ST-SBE, a very short training sequence is used to provide a rough initial least squares Estimate of the weight vector. An efficient modified Newton method (MNM) for minimizing the established cost function is proposed to fast search the optimal weight vector. Very interestingly, we prove that the proposed MNM has the same quadratic order of convergence as Newton methods. In addition, the proposed MNM has much lower computational complexity than Newton methods. Simulation results are provided to demonstrate that the ST-SBE has better performances than the gradient-Newton (GN)-based concurrent constant modulus algorithm (CMA) with SDD scheme (GN-CMA+SDD).
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a modified method for closed loop identification of transfer function models
IEEE Transactions on Circuits and Systems I-regular Papers, 2002Co-Authors: Wei Xing ZhengAbstract:Substantial revisions on the newly proposed bias correction based method are made in the framework of indirect identification of a linear (possibly unstable) plant operating in closed loop with a low-order stabilizing controller. By making a new formulation of a Least-Squares Estimate of an intermediate parameter vector purposely introduced, the modified algorithm is able to achieve a direct yet unbiased closed-loop system Estimate in the presence of misspecified noise model. With no identification of a high-order augmented closed-loop system, the computational complexity of the algorithm is significantly reduced. Simulations of identifying an open-loop unstable plant illustrate the promising performance of the modified algorithm in low signal-to-noise ratio environments.
Dragan Jukic - One of the best experts on this subject based on the ideXlab platform.
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on nonlinear weighted total least squares parameter estimation problem for the three parameter weibull density
Applied Mathematical Modelling, 2010Co-Authors: Darija Markovic, Dragan JukicAbstract:Abstract The three-parameter Weibull density function is widely employed as a model in reliability and lifetime studies. Estimation of its parameters has been approached in the literature by various techniques, because a standard maximum likelihood Estimate does not exist. In this paper we consider the nonlinear weighted total least squares fitting approach. As a main result, a theorem on the existence of the total least squares Estimate is obtained, as well as its generalization in the total l q norm ( q ⩾ 1 ). Some numerical simulations to support the theoretical work are given.
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nonlinear weighted least squares estimation of a three parameter weibull density with a nonparametric start
Journal of Computational and Applied Mathematics, 2009Co-Authors: Darija Markovic, Dragan Jukic, Mirta BensicAbstract:This paper is concerned with the parameter estimation problem for the three-parameter Weibull density which is widely employed as a model in reliability and lifetime studies. Our approach is a combination of nonparametric and parametric methods. The basic idea is to start with an initial nonparametric density Estimate which needs to be as good as possible, and then apply the nonlinear least squares method to Estimate the unknown parameters. As a main result, a theorem on the existence of the least squares Estimate is obtained. Some simulations are given to show that our approach is satisfactory if the initial density is of good enough quality.
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on the existence of the nonlinear weighted least squares Estimate for a three parameter weibull distribution
Computational Statistics & Data Analysis, 2008Co-Authors: Dragan Jukic, Mirta Bensic, Rudolf ScitovskiAbstract:The problem of nonlinear weighted least squares fitting of the three-parameter Weibull distribution to the given data (wi,ti,yi), i=1,...,n, is considered. The part wi>0 of the data stands for the data weights. It is shown that the best least squares Estimate exists provided that the data satisfy just the following two natural conditions: (i) 0
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least squares fitting gaussian type curve
Applied Mathematics and Computation, 2005Co-Authors: Dragan Jukic, Rudolf ScitovskiAbstract:Given the data (p"i,t"i,y"i), i=1,...,m, m>=3, we give necessary and sufficient conditions which guarantee the existence of the weighted least squares Estimate for a Gaussian type function. To this end, we suggest a choice of the suitable initial approximation for an iterative minimization, and give some numerical examples.