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33
On Bayesian analysis of mixtures with an unknown number of components
 INSTITUTE OF INTERNATIONAL ECONOMICS PROJECT ON INTERNATIONAL COMPETITION POLICY,&QUOT; COM/DAFFE/CLP/TD(94)42
, 1997
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Model selection for probabilistic clustering using crossvalidated likelihood
 Statistics and computing
, 2000
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Assessing model mimicry using the parametric bootstrap
 Journal of Mathematical Psychology
, 2004
"... We present a general sampling procedure to quantify model mimicry, defined as the ability of a model to account for data generated by a competing model. This sampling procedure, called the parametric bootstrap crossfitting method (PBCM; cf. Williams (J. R. Statist. Soc. B 32 (1970) 350; Biometrics ..."
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Cited by 37 (5 self)
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We present a general sampling procedure to quantify model mimicry, defined as the ability of a model to account for data generated by a competing model. This sampling procedure, called the parametric bootstrap crossfitting method (PBCM; cf. Williams (J. R. Statist. Soc. B 32 (1970) 350; Biometrics 26 (1970) 23)), generates distributions of differences in goodnessoffit expected under each of the competing models. In the data informed version of the PBCM, the generating models have specific parameter values obtained by fitting the experimental data under consideration. The data informed difference distributions can be compared to the observed difference in goodnessoffit to allow a quantification of model adequacy. In the data uninformed version of the PBCM, the generating models have a relatively broad range of parameter values based on prior knowledge. Application of both the data informed and the data uninformed PBCM is illustrated with several examples. r 2003 Elsevier Inc. All rights reserved. 1.
Bayesian Statistics
 in WWW', Computing Science and Statistics
, 1989
"... ∗ Signatures are on file in the Graduate School. This dissertation presents two topics from opposite disciplines: one is from a parametric realm and the other is based on nonparametric methods. The first topic is a jackknife maximum likelihood approach to statistical model selection and the second o ..."
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Cited by 32 (1 self)
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∗ Signatures are on file in the Graduate School. This dissertation presents two topics from opposite disciplines: one is from a parametric realm and the other is based on nonparametric methods. The first topic is a jackknife maximum likelihood approach to statistical model selection and the second one is a convex hull peeling depth approach to nonparametric massive multivariate data analysis. The second topic includes simulations and applications on massive astronomical data. First, we present a model selection criterion, minimizing the KullbackLeibler distance by using the jackknife method. Various model selection methods have been developed to choose a model of minimum KullbackLiebler distance to the true model, such as Akaike information criterion (AIC), Bayesian information criterion (BIC), Minimum description length (MDL), and Bootstrap information criterion. Likewise, the jackknife method chooses a model of minimum KullbackLeibler distance through bias reduction. This bias, which is inevitable in model
Asymptotic behaviour of the posterior distribution in overfitted mixture models
, 2010
"... mixture models ..."
Penalized Maximum Likelihood Estimator for Normal Mixtures
, 2000
"... The estimation of the parameters of a mixture of Gaussian densities is considered, within the framework of maximum likelihood. Due to unboundedness of the likelihood function, the maximum likelihood estimator fails to exist. We adopt a solution to likelihood function degeneracy which consists in pen ..."
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Cited by 21 (3 self)
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The estimation of the parameters of a mixture of Gaussian densities is considered, within the framework of maximum likelihood. Due to unboundedness of the likelihood function, the maximum likelihood estimator fails to exist. We adopt a solution to likelihood function degeneracy which consists in penalizing the likelihood function. The resulting penalized likelihood function is then bounded over the parameter space and the existence of the penalized maximum likelihood estimator is granted. As original contribution we provide asymptotic properties, and in particular a consistency proof, for the penalized maximum likelihood estimator. Numerical examples are provided in the finite data case, showing the performances of the penalized estimator compared to the standard one.
Modeling and testing for heterogeneity in observed strategic behavior
 Review of Economics and Statistics
, 1998
"... Experimental data have consistently shown diversity in beliefs as well as in actions among experimental subjects. This paper presents and compares alternative behavioral econometric models for the characterization of player heterogeneity, both between subpopulations of players and within subpopulat ..."
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Cited by 20 (6 self)
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Experimental data have consistently shown diversity in beliefs as well as in actions among experimental subjects. This paper presents and compares alternative behavioral econometric models for the characterization of player heterogeneity, both between subpopulations of players and within subpopulations. In particular, two econometric models of diversity within subpopulations of players are investigated: one using a model of computational errors and the other allowing for diversity in prior beliefs around a modal prior for the subpopulation.
Mixed normal conditional heteroskedasticity
 Journal of Financial Econometrics
, 2004
"... Both unconditional mixednormal distributions and GARCH models with fattailed conditional distributions have been employed for modeling financial return data. We consider a mixednormal distribution coupled with a GARCHtype structure which allows for conditional variance in each of the components ..."
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Cited by 16 (3 self)
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Both unconditional mixednormal distributions and GARCH models with fattailed conditional distributions have been employed for modeling financial return data. We consider a mixednormal distribution coupled with a GARCHtype structure which allows for conditional variance in each of the components as well as dynamic feedback between the components. Special cases and relationships with previously proposed specifications are discussed and stationarity conditions are derived. An empirical application to NASDAQindex data indicates the appropriateness of the model class and illustrates that the approach can generate a plausible disaggregation of the conditional variance process, in which the components ’ volatility dynamics have a clearly distinct behavior that is, for example, compatible with the wellknown leverage effect.
The likelihood ratio test for the number of components in a mixture with Markov regime. ESAIM Probability and statistics 4
, 2000
"... Abstract. We study the LRT statistic for testing a single population i.i.d. model against a mixture of two populations with Markov regime. We prove that the LRT statistic converges to innity in probability as the number of observations tends to innity. This is a consequence of a convergence result o ..."
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Cited by 14 (5 self)
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Abstract. We study the LRT statistic for testing a single population i.i.d. model against a mixture of two populations with Markov regime. We prove that the LRT statistic converges to innity in probability as the number of observations tends to innity. This is a consequence of a convergence result of the LRT statistic for a subproblem where the parameters are restricted to a subset of the whole parameter set. Resume. Nous etudions la statistique du test de rapport de vraisemblance (TRV) pour tester un modele i.i.d. a une population contre un melange de deux populations a regime markovien. Nous prouvons que la statistique du TRV converge vers l’inni en probabilite quand la taille de l’echantillon tend vers l’inni. Ceci est une consequence d’un resultat de convergence de la statistique du TRV pour un sousprobleme ou les parametres sont restreints a un sousensemble de l’ensemble complet des parametres.
A latent Markov model for detecting patterns of criminal activity
 J. R. Statist. Soc. A
, 2007
"... We propose a latent Markov (LM) approach for modelling offending patterns taking into account the nature and the sequence of offences the approach is applied to the England and Wales Offenders Index dataset, which has the following features it a court based record of the criminal histories of all of ..."
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Cited by 10 (6 self)
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We propose a latent Markov (LM) approach for modelling offending patterns taking into account the nature and the sequence of offences the approach is applied to the England and Wales Offenders Index dataset, which has the following features it a court based record of the criminal histories of all offenders in England and Wales from 1963 to the current day general population sample of n = 4, 639 individuals paroled from the cohort of those born in 1953 (males =3,762, females=877), and followed through to 1993 offences are combined into J = 10 major categories described in