Factor analysis by the method of maximum likelihood
A. Kieloch, W. Oktaba (1971)
Applicationes Mathematicae
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A. Kieloch, W. Oktaba (1971)
Applicationes Mathematicae
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Mariusz Grządziel, Andrzej Michalski (2014)
Discussiones Mathematicae Probability and Statistics
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In the paper, the problem of the existence of the maximum likelihood estimate and the REML estimate in the variance components model is considered. Errors in the proof of Theorem 3.1 in the article of Demidenko and Massam (Sankhyā 61, 1999), giving a necessary and sufficient condition for the existence of the maximum likelihood estimate in this model, are pointed out and corrected. A new proof of Theorem 3.4 in the Demidenko and Massam's article, concerning the existence of the REML...
Baklizi, Ayman, Daud, Isa, Ibrahim, Noor Akma (1999)
Bulletin of the Malaysian Mathematical Society. Second Series
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Vivek S. Borkar (1985)
Banach Center Publications
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Youngjo Lee, John A. Nelder (2005)
SORT
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For inferences from random-effect models Lee and Nelder (1996) proposed to use hierarchical likelihood (h-likelihood). It allows influence from models that may include both fixed and random parameters. Because of the presence of unobserved random variables h-likelihood is not a likelihood in the Fisherian sense. The Fisher likelihood framework has advantages such as generality of application, statistical and computational efficiency. We introduce an extended likelihood framework and...
Ivo Vrkoč (1969)
Czechoslovak Mathematical Journal
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Estelle Kuhn, Marc Lavielle (2004)
ESAIM: Probability and Statistics
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The stochastic approximation version of EM (SAEM) proposed by Delyon et al. (1999) is a powerful alternative to EM when the E-step is intractable. Convergence of SAEM toward a maximum of the observed likelihood is established when the unobserved data are simulated at each iteration under the conditional distribution. We show that this very restrictive assumption can be weakened. Indeed, the results of Benveniste et al. for stochastic approximation with markovian perturbations are used...
Ewa Bakinowska, Radosław Kala (2004)
Discussiones Mathematicae Probability and Statistics
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In the paper two approaches to the problem of estimation of transition probabilities are considered. The approach by McCullagh and Nelder [5], based on the independent model and the quasi-likelihood function, is compared with the approach based on the marginal model and the standard likelihood function. The estimates following from these two approaches are illustrated on a simple example which was used by McCullagh and Nelder.
Mariusz Grządziel (2014)
Discussiones Mathematicae Probability and Statistics
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In the paper we deal with the problem of parameter estimation in the linear normal mixed model with two variance components. We present solutions to the problem of finding the global maximizer of the likelihood function and to the problem of finding the global maximizer of the REML likelihood function in this model.
Daniel Commenges (2003)
SORT
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We consider the mixed dicrete-continuous pattern of observation in a multi-state model; this is a classical pattern because very often clinical status is assessed at discrete visit times while time of death is observed exactly. The likelihood can easily be written heuristically for such models. However a formal proof is not easy in such observational patterns. We give a rigorous derivation al the likelihood for the illness-death model based on applying Jacod´s formula to an observed...