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Global Optimization of Statistical Functions with Simulated Annealing
 Journal of Econometrics
, 1994
"... Many statistical methods rely on numerical optimization to estimate a model’s parameters. Unfortunately, conventional algorithms sometimes fail. Even when they do converge, there is no assurance that they have found the global, rather than a local, optimum. We test a new optimization algorithm, simu ..."
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Cited by 198 (2 self)
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Many statistical methods rely on numerical optimization to estimate a model’s parameters. Unfortunately, conventional algorithms sometimes fail. Even when they do converge, there is no assurance that they have found the global, rather than a local, optimum. We test a new optimization algorithm, simulated annealing, on four econometric problems and compare it to three common conventional algorithms. Not only can simulated annealing find the global optimum, it is also less likely to fail on difficult functions because it is a very robust algorithm. The promise of simulated annealing is demonstrated on the four econometric problems.
ESTIMATION OF INCOME DISTRIBUTION AND DETECTION OF SUBPOPULATIONS: AN EXPLANATORY MODEL
, 2003
"... Inequality and polarization analyses are complementary but conceptually different. They are usually implemented independently in practice, with different a priori assumptions and different tools. In this paper, we develop a unique method to study simultaneously these different and complementary conc ..."
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Cited by 3 (0 self)
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Inequality and polarization analyses are complementary but conceptually different. They are usually implemented independently in practice, with different a priori assumptions and different tools. In this paper, we develop a unique method to study simultaneously these different and complementary concerns. Based on mixture models, the method we develop includes at the same time: an estimation of income distribution with no a priori assumptions a decomposition in several homogeneous subpopulations an explanatory model to study the structure of the income distribution.
On tests for global maximum of the loglikelihood function
 IEEE Trans. Inform. Theory
, 2004
"... Abstract — Given the location of a relative maximum of the loglikelihood function, how to assess whether it is the global maximum? This paper investigates a statistical tool, which answers this question by posing it as a hypothesis testing problem. A general framework for constructing tests for glo ..."
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Cited by 2 (1 self)
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Abstract — Given the location of a relative maximum of the loglikelihood function, how to assess whether it is the global maximum? This paper investigates a statistical tool, which answers this question by posing it as a hypothesis testing problem. A general framework for constructing tests for global maximum is given. The characteristics of the tests are investigated for two cases: correctly specified model and model mismatch. A finite sample approximation to the power is given, which gives a tool for performance prediction and a measure for comparison between tests. The sensitivity of the tests to model mismatch is analyzed in terms of the Renyi divergence and the KullbackLeibler distance between the true underlying distribution and the assumed parametric class and tests that are insensitive to small deviations from the model are derived. The tests are illustrated for three applications: passive localization or direction finding using an array of sensors, estimating the parameters of a Gaussian mixture model, and estimation of superimposed exponentials in noise problems that are known to suffer from local maxima. Index Terms — Parameter estimation, maximum likelihood, global optimization, local maxima, array processing, Gaussian
ADAPTIVE SENSING IN UNCERTAIN ENVIRONMENTS: MAXIMUM LIKELIHOOD, SENSOR NETWORKS, AND REINFORCEMENT LEARNING
, 2006
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EM algorithm and Varible Neighborhood Search for fitting Finite Mixture Model parameters
, 2009
"... Finding maximum likelihood parameter values for Finite Mixture Model (FMM) is often done with the Expectation Maximization (EM) algorithm. However the choice of initial values can severely affect the time to attain convergence of the algorithm and its efficiency in finding global maxima. We allevia ..."
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Finding maximum likelihood parameter values for Finite Mixture Model (FMM) is often done with the Expectation Maximization (EM) algorithm. However the choice of initial values can severely affect the time to attain convergence of the algorithm and its efficiency in finding global maxima. We alleviate this defect by embedding the EM algorithm within the variable Neighborhood Search (VNS) methaheurestic framework. Computational experiment in several problems in literature as well as some larger ones are reported.
unknown title
, 2002
"... www.elsevier.com/locate/csda Choosing initial values for the EM algorithm for)nite mixtures ..."
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www.elsevier.com/locate/csda Choosing initial values for the EM algorithm for)nite mixtures
Estimation of the Income Distribution and Detection of Subpopulations: an Explanatory Model
"... Empirical evidence, obtained from nonparametric estimation of the income distribution, exhibits strong heterogeneity in most populations of interest. It is common, therefore, to suspect that the population is composed of several homogeneous subpopulations. Such an assumption leads us to consider m ..."
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Empirical evidence, obtained from nonparametric estimation of the income distribution, exhibits strong heterogeneity in most populations of interest. It is common, therefore, to suspect that the population is composed of several homogeneous subpopulations. Such an assumption leads us to consider mixed income distributions whose components feature the distributions of the incomes of a particular homogeneous subpopulation. A model with mixing probabilities that are allowed to vary with exogenous individual variables that characterize each subpopulation is developed. This model simultaneously provides a flexible estimation of the income distribution, a breakdown into several subpopulations and an explanation of income heterogeneity. Key words: income distribution, mixture models. 1