scholarly journals Estimation of Multilevel Simultaneous Equation Models through Genetic Algorithms

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2098
Author(s):  
Rocío Hernández-Sanjaime ◽  
Martín González ◽  
Jose J. López-Espín
Keyword(s):  
Maximum Likelihood ◽  
Covariance Structure ◽  
Likelihood Estimation ◽  
Optimization Method ◽  
Simultaneous Equation ◽  
Equation Model ◽  
Tuning Parameters ◽  
Hybrid Metaheuristic ◽  
Error Terms ◽  
Simultaneous Equation Models

Problems in estimating simultaneous equation models when error terms are not intertemporally uncorrelated has motivated the introduction of a new multivariate model referred to as Multilevel Simultaneous Equation Model (MSEM). The maximum likelihood estimation of the parameters of an MSEM has been set forth. Because of the difficulties associated with the solution of the system of likelihood equations, the maximum likelihood estimator cannot be obtained through exhaustive search procedures. A hybrid metaheuristic that combines a genetic algorithm and an optimization method has been developed to overcome both technical and analytical limitations in the general case when the covariance structure is unknown. The behaviour of the hybrid metaheuristic has been discussed by varying different tuning parameters. A simulation study has been included to evaluate the adequacy of this estimator when error terms are not serially independent. Finally, the performance of this estimation approach has been compared with regard to other alternatives.

scholarly journals A Geometric Calibration Method of Hydrophone Array Based on Maximum Likelihood Estimation with Sources in Near Field

2020 ◽  
Vol 8 (9) ◽  
pp. 678
Author(s):  
Nan Zou ◽  
Zhenqi Jia ◽  
Jin Fu ◽  
Jia Feng ◽  
Mengqi Liu
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Signal To Noise Ratio ◽  
Near Field ◽  
Likelihood Estimation ◽  
Calibration Method ◽  
Optimization Method ◽  
High Signal ◽  
Geometric Calibration ◽  
Environment Experiment

Considering the requirement of the near-field calibration under strong underwater multipath condition, a high-precision geometric calibration method based on maximum likelihood estimation is proposed. It can be used as both auxiliary-calibration and self-calibration. According to the near-field geometry error model, the objective function of nonlinear optimization problem is constructed by using the unconditional maximum likelihood estimator. The influence of multipath on geometric calibration is studied. The strong reflections are considered as the coherent sources, and the compensation strategy for auxiliary-calibration is realized. The optimization method (differential evolution, DE) is used to solve the geometry errors and sources’ position. The method in this paper is compared with the eigenvector method. The simulation results show that the method in this paper is more accurate than the eigenvector method especially under high signal-to-noise ratio (SNR) and multipath environment. Experiment results further verify the effectiveness.

scholarly journals Bayesian estimation of simultaneous equation model with lagged endogenous variables and first order serially correlated errors

2018 ◽  
Vol 24 (2) ◽  
pp. 235-244
Author(s):  
Adedayo A Adepoju ◽  
Oluwayemisi O, Alaba ◽  
P Ogundunmadetayo
Keyword(s):  
Bayesian Estimation ◽  
Simultaneous Equation ◽  
Equation Model ◽  
Bayesian Estimator ◽  
Simultaneous Equation Model ◽  
Correlated Errors ◽  
First Order ◽  
Endogenous Variables ◽  
Standard Deviations ◽  
Simultaneous Equation Models

Most simultaneous equation models involve the inclusion of lagged endogenous and/or exogenous variables and sometimes it may be misleading to assume that the errors are normally distributed when in reality they exhibit functional formsthat are not normal especially in practical situations. The classical methods of estimating parameters of simultaneous equation models are usually affected by the presence of autocorrelation among the error terms. Unfortunately, in practice the form of correlation between the pairs of the random deviates is unknown.In this paper classical and Bayesian methods for the estimation of simultaneous equation model withlagged endogenous variables and first order serially correlated errors are considered. The smallsample properties of the methods at different levels of correlation for ρ = 0.2, 0.5 and 0.8are compared.Better parameter estimates were produced by the Bayesian estimator with smaller standard errors compared to the classical method. The standard deviations of the Bayesian estimator are consistently better than those of the OLS estimator for the sample sizes considered. For example, the standard deviations of the Bayesian for b14 (the coefficient of the lagged endogenous variable,y 1t-1) when ρ = 0.2 at N = 10, 15, 20 and 25 were 0.07712781, 0.05433923, 0.03230012 and 0.03177252 respectively while those of OLS were 0.0784732, 0.4718914, 0.05701936 and 1.31422868. However, when ρ = 0.8, the standard deviations were 0.0548055, 0.03860254, 0.02572899 and 0.02126175 for Bayesian and 0.0562190, 0.03882345, 0.053676 and 0.0315632 for OLS. Interestingly, notice that even at high correlation level, the estimates produced by the Bayesian method are closer to the parameter values and the standard deviations decrease as the sample size increases. Hence, the Bayesian estimation method might be a better choice when lagged endogenous variables are included in a simultaneous equation model with auto-correlated disturbances since it appeared to give better results compared to the classical approach.Keywords: Bayesian estimation, Lagged endogenous variables, Simultaneous equations, Monte-Carlo Simulation, First-order autoregressive process.

scholarly journals On estimation in multilevel models with block circular symmetric covariance structure

2012 ◽  
Vol 16 (1) ◽  
pp. 83-96
Author(s):  
Yuli Liang ◽  
Dietrich von Rosen ◽  
Tatjana von Rosen
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Parameter Space ◽  
Variance Components ◽  
Multilevel Model ◽  
Multilevel Models ◽  
Covariance Structure ◽  
Maximum Likelihood Estimators ◽  
Likelihood Estimation

In this article we consider a multilevel model with block circular symmetric covariance structure. Maximum likelihood estimation of the parameters of this model is discussed. We show that explicit maximum likelihood estimators of variance components exist under certain restrictions on the parameter space.

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