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Cheng-der Fuh - One of the best experts on this subject based on the ideXlab platform.

  • Reply to “On some problems in the article Efficient Likelihood Estimation in State Space Models” by Cheng-Der Fuh [Ann. Statist. 34 (2006) 2026–2068]
    The Annals of Statistics, 2010
    Co-Authors: Cheng-der Fuh
    Abstract:

    Motivated by studying asymptotic properties of the maximum Likelihood estimator (MLE) in stochastic volatility (SV) models, in this paper we investigate Likelihood estimation in state space models. We first prove, under some regularity conditions, there is a consistent sequence of roots of the Likelihood Equation that is asymptotically normal with the inverse of the Fisher information as its variance. With an extra assumption that the Likelihood Equation has a unique root for each $n$, then there is a consistent sequence of estimators of the unknown parameters. If, in addition, the supremum of the log Likelihood function is integrable, the MLE exists and is strongly consistent. Edgeworth expansion of the approximate solution of Likelihood Equation is also established. Several examples, including Markov switching models, ARMA models, (G)ARCH models and stochastic volatility (SV) models, are given for illustration.Comment: With the comments by Jens Ledet Jensen and reply to the comments. Published at http://dx.doi.org/10.1214/009053606000000614; http://dx.doi.org/10.1214/09-AOS748A; http://dx.doi.org/10.1214/09-AOS748B in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

  • Efficient Likelihood estimation in state space models
    The Annals of Statistics, 2006
    Co-Authors: Cheng-der Fuh
    Abstract:

    Motivated by studying asymptotic properties of the maximum Likelihood estimator (MLE) in stochastic volatility (SV) models, in this paper we investigate Likelihood estimation in state space models. We first prove, under some regularity conditions, there is a consistent sequence of roots of the Likelihood Equation that is asymptotically normal with the inverse of the Fisher information as its variance. With an extra assumption that the Likelihood Equation has a unique root for each n, then there is a consistent sequence of estimators of the unknown parameters. If, in addition, the supremum of the log Likelihood function is integrable, the MLE exists and is strongly consistent. Edge-worth expansion of the approximate solution of Likelihood Equation is also established. Several examples, including Markov switching models, ARMA models, (G)ARCH models and stochastic volatility (SV) models, are given for illustration.

Alberto Tannus - One of the best experts on this subject based on the ideXlab platform.

  • a novel pseudo Likelihood Equation for potts mrf model parameter estimation in image analysis
    International Conference on Image Processing, 2008
    Co-Authors: Alexandre L M Levada, Nelson D A Mascarenhas, Alberto Tannus
    Abstract:

    This paper presents a novel pseudo-Likelihood Equation for the estimation of the Potts MRF model parameter on second-order neighborhood systems, allowing the modeling of less restrictive contextual systems in a large number of MRF applications in a computationally feasible way. We propose a hypothesis testing approach to validate the obtained results. The test statistic together with the p-values, calculated through our approximation for the asymptotic variance of the derived maximum pseudo-Likelihood estimator, provide a complete framework for quantitative analysis in MRF parameter estimation.

  • ICIP - A novel pseudo-Likelihood Equation for Potts MRF model parameter estimation in image analysis
    2008 15th IEEE International Conference on Image Processing, 2008
    Co-Authors: Alexandre L M Levada, Nelson D A Mascarenhas, Alberto Tannus
    Abstract:

    This paper presents a novel pseudo-Likelihood Equation for the estimation of the Potts MRF model parameter on second-order neighborhood systems, allowing the modeling of less restrictive contextual systems in a large number of MRF applications in a computationally feasible way. We propose a hypothesis testing approach to validate the obtained results. The test statistic together with the p-values, calculated through our approximation for the asymptotic variance of the derived maximum pseudo-Likelihood estimator, provide a complete framework for quantitative analysis in MRF parameter estimation.

Bezza Hafidi - One of the best experts on this subject based on the ideXlab platform.

  • An Approximation Method for a Maximum Likelihood Equation System and Application to the Analysis of Accidents Data
    Open Journal of Statistics, 2017
    Co-Authors: Assi N'guessan, Issa Cherif Geraldo, Bezza Hafidi
    Abstract:

    There exist many iterative methods for computing the maximum Likelihood estimator but most of them suffer from one or several drawbacks such as the need to inverse a Hessian matrix and the need to find good initial approximations of the parameters that are unknown in practice. In this paper, we present an estimation method without matrix inversion based on a linear approximation of the Likelihood Equations in a neighborhood of the constrained maximum Likelihood estimator. We obtain closed-form approximations of solutions and standard errors. Then, we propose an iterative algorithm which cycles through the components of the vector parameter and updates one component at a time. The initial solution, which is necessary to start the iterative procedure, is automated. The proposed algorithm is compared to some of the best iterative optimization algorithms available on R and MATLAB software through a simulation study and applied to the statistical analysis of a road safety measure.

  • An Approximation Method for a Maximum Likelihood Equation System and Application to the Analysis of Accidents Data
    Open Journal of Statistics, 2017
    Co-Authors: Assi N’guessan, Issa Cherif Geraldo, Bezza Hafidi
    Abstract:

    International audienceThere exist many iterative methods for computing the maximum Likelihood estimator but most of them suffer from one or several drawbacks such as the need to inverse a Hessian matrix and the need to find good initial approximations of the parameters that are unknown in practice. In this paper, we present an estimation method without matrix inversion based on a linear approximation of the Likelihood Equations in a neighborhood of the constrained maximum Likelihood estimator. We obtain closed-form approximations of solutions and standard errors. Then, we propose an iterative algorithm which cycles through the components of the vector parameter and updates one component at a time. The initial solution, which is necessary to start the iterative procedure, is automated. The proposed algorithm is compared to some of the best iterative optimization algorithms available on R and MATLAB software through a simulation study and applied to the statistical analysis of a road safety measure

Ryszard Magiera - One of the best experts on this subject based on the ideXlab platform.

  • Sequential Estimation through Estimating Equations
    Operations Research ’93, 1994
    Co-Authors: Ryszard Magiera
    Abstract:

    Using the approach to estimation through estimating Equations, the information inequalities for regular sequential estimating plans are given and an optimum property of regular maximum Likelihood sequential plans is shown in a general model for stochastic processes. The optimum sequential estimating functions are obtained in the nuisance parameter case as well. Under suitable regularity conditions on stopping times and Likelihood functions it is pointed out that in searching for optimum sequential estimators one can replace the maximum Likelihood Equation by the maximum conditional Likelihood Equation in order to eliminate the influence of the nuisance parameter.

Peter X K Song - One of the best experts on this subject based on the ideXlab platform.

  • multivariate dispersion models generated from gaussian copula
    Scandinavian Journal of Statistics, 2000
    Co-Authors: Peter X K Song
    Abstract:

    In this paper a class of multivariate dispersion models generated from the multivariate Gaussian copula is presented. Being a multivariate extension of Jorgensen's (1987a) dispersion models, this class of multivariate models is parametrized by marginal position, dispersion and dependence parameters, producing a large variety of multivariate discrete and continuous models including the multivariate normal as a special case. Properties of the multivariate distributions are investigated, some of which are similar to those of the multivariate normal distribution, which makes these models potentially useful for the analysis of correlated non-normal data in a way analogous to that of multivariate normal data. As an example, we illustrate an application of the models to the regression analysis of longitudinal data, and establish an asymptotic relationship between the Likelihood Equation and the generalized estimating Equation of Liang & Zeger (1986).