It is quite common to encounter compositional data in a regression framework in data analysis. When both responses and predictors are compositional, most existing models rely on a family of log-ratio based transformat...
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It is quite common to encounter compositional data in a regression framework in data analysis. When both responses and predictors are compositional, most existing models rely on a family of log-ratio based transformations to move the analysis from the simplex to the reals. This often makes the interpretation of the model more complex. A transformation-free regression model was recently developed, but it only allows for a single compositional predictor. However, many datasets include multiple compositional predictors of interest. Motivated by an application to hydrothermal liquefaction (HTL) data, a novel extension of this transformation-free regression model is provided that allows for two (or more) compositional predictors to be used via a latent variable mixture. A modified expectation-maximization algorithm is proposed to estimate model parameters, which are shown to have natural interpretations. Conformal inference is used to obtain prediction limits on the compositional response. The resulting methodology is applied to the HTL dataset. Extensions to multiple predictors are discussed.
The main objective of this paper is to discuss maximum likelihood inference for the comparative structural calibration model (Barnett, in Biometrics 25:129-142, 1969), which is frequently used in the problem of assess...
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The main objective of this paper is to discuss maximum likelihood inference for the comparative structural calibration model (Barnett, in Biometrics 25:129-142, 1969), which is frequently used in the problem of assessing the relative calibrations and relative accuracies of a set of p instruments, each designed to measure the same characteristic on a common group of n experimental units. We consider asymptotic tests to answer the outlined questions. The methodology is applied to a real data set and a small simulation study is presented.
Recently, different mixture models have been proposed for multilevel data, generally requiring the local independence assumption. In this work, this assumption is relaxed by allowing each mixture component at the lowe...
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Recently, different mixture models have been proposed for multilevel data, generally requiring the local independence assumption. In this work, this assumption is relaxed by allowing each mixture component at the lower level of the hierarchical structure to be modeled according to a multivariate Gaussian distribution with a non-diagonal covariance matrix. For high-dimensional problems, this solution can lead to highly parameterized models. In this proposal, the trade-off between model parsimony and flexibility is governed by assuming a latent factor generative model. (c) 2010 Elsevier Inc. All rights reserved.
The majority of the existing literature on model-based clustering deals with symmetric components. In some cases, especially when dealing with skewed subpopulations, the estimate of the number of groups can be mislead...
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The majority of the existing literature on model-based clustering deals with symmetric components. In some cases, especially when dealing with skewed subpopulations, the estimate of the number of groups can be misleading;if symmetric components are assumed we need more than one component to describe an asymmetric group. Existing mixture models, based on multivariate normal distributions and multivariate t distributions, try to fit symmetric distributions, i.e. they fit symmetric clusters. In the present paper, we propose the use of finite mixtures of the normal inverse Gaussian distribution (and its multivariate extensions). Such finite mixture models start from a density that allows for skewness and fat tails, generalize the existing models, are tractable and have desirable properties. We examine both the univariate case, to gain insight, and the multivariate case, which is more useful in real applications. em type algorithms are described for fitting the models. Real data examples are used to demonstrate the potential of the new model in comparison with existing ones.
We propose the scale mixtures of multivariate skew-normal-Cauchy distributions as a new class of asymmetric heavy-tailed distributions. We derive an emalgorithm for maximum likelihood estimation. (C) 2017 Elsevier B....
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We propose the scale mixtures of multivariate skew-normal-Cauchy distributions as a new class of asymmetric heavy-tailed distributions. We derive an emalgorithm for maximum likelihood estimation. (C) 2017 Elsevier B.V. All rights reserved.
This paper presents a new class of models for persons-by-items data. The essential new feature of this class is the representation of the persons: every person is represented by its membership to multiple latent class...
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This paper presents a new class of models for persons-by-items data. The essential new feature of this class is the representation of the persons: every person is represented by its membership to multiple latent classes, each of which belongs to one latent classification. The models can be considered as a formalization of the hypothesis that the responses come about in a process that involves the application of a number of mental operations. Two algorithms for maximum likelihood (ML) and maximum a posteriori (MAP) estimation are described. They both make use of the tractability of the complete data likelihood to maximize the observed data likelihood. Properties of the MAP estimators (i.e., uniqueness and goodness-of-recovery) and the existence of asymptotic standard errors were examined in a simulation study. Then, one of these models is applied to the responses to a set of fraction addition problems. Finally, the models are compared to some related models in the literature.
We consider the estimation of the transition matrix of a hidden Markovian process by using information geometry with respect to transition matrices. In this paper, only the histogram of k-memory data is used for the e...
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We consider the estimation of the transition matrix of a hidden Markovian process by using information geometry with respect to transition matrices. In this paper, only the histogram of k-memory data is used for the estimation. To establish our method, we focus on a partial observation model with the Markovian process and we propose an efficient estimator whose asymptotic estimation error is given as the inverse of projective Fisher information of transition matrices. This estimator is applied to the estimation of the transition matrix of the hidden Markovian process. In this application, we carefully discuss the equivalence problem for hidden Markovian process on the tangent space.
Using play-by-play data from the very beginning of the professional football league in Turkey, a semi-Markov model is presented for describing the performance of football teams. The official match results of the selec...
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Using play-by-play data from the very beginning of the professional football league in Turkey, a semi-Markov model is presented for describing the performance of football teams. The official match results of the selected teams during 55 football seasons are used and winning, drawing and losing are considered as Markov states. The semi-Markov model is constructed with transition rates inferred from the official match results. The duration between the last match of a season and the very first match of the following season is much longer than any other duration during the season. Therefore these values are considered as missing values and estimated by using expectation-maximization algorithm. The effect of the sojourn time in a state to the performance of a team is discussed as well as mean sojourn times after losing/winning are estimated. The limiting probabilities of winning, drawing and losing are calculated. Some insights about the performance of the selected teams are presented.
In the paper we introduce a method of computing M-estimators in a mixed unbalanced model. The algorithm is based on weighted loglikelihood. It simultaneously finds the estimator of location and scale. Convergence of t...
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In the paper we introduce a method of computing M-estimators in a mixed unbalanced model. The algorithm is based on weighted loglikelihood. It simultaneously finds the estimator of location and scale. Convergence of the algorithm to a solution of M-equations is proved and a simulation study is given.
With a view to statistical inference for discretely observed diffusion models, we propose simple methods of simulating diffusion bridges, approximately and exactly. Diffusion bridge simulation plays a fundamental role...
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With a view to statistical inference for discretely observed diffusion models, we propose simple methods of simulating diffusion bridges, approximately and exactly. Diffusion bridge simulation plays a fundamental role in likelihood and Bayesian inference for diffusion processes. First a simple method of simulating approximate diffusion bridges is proposed and studied. Then these approximate bridges are used as proposal for an easily implemented Metropolis Hastings algorithm that produces exact diffusion bridges. The new method utilizes time-reversibility properties of one-dimensional diffusions and is applicable to all one-dimensional diffusion processes with finite speed-measure. One advantage of the new approach is that simple simulation methods like the Milstein scheme can be applied to bridge simulation. Another advantage over previous bridge simulation methods is that the proposed method works well for diffusion bridges in long intervals because the computational complexity of the method is linear in the length of the interval. For p-mixing diffusions the approximate method is shown to be particularly accurate for long time intervals. In a simulation study, we investigate the accuracy and efficiency of the approximate method and compare it to exact simulation methods. In the study, our method provides a very good approximation to the distribution of a diffusion bridge for bridges that are likely to occur in applications to statistical inference. To illustrate the usefulness of the new method, we present an em-algorithm for a discretely observed diffusion process.
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