Toeplitz covariance matrix estimation has many uses in statistical signal processing due to the stationarity assumption of many signals. For some applications, further constraints may exist on the maximum lag at which...
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ISBN:
(纸本)1424407281
Toeplitz covariance matrix estimation has many uses in statistical signal processing due to the stationarity assumption of many signals. For some applications, further constraints may exist on the maximum lag at which the correlation function is non-zero and thereby giving rise to a band-Toeplitz covariance matrix. In this paper, an existing em-algorithm for Toeplitz estimation is generalized to the case of band-Toeplitz estimation. In addition, the Cramer-Rao lower-bound for unbiased band-Toeplitz covariance matrix estimation is derived and through simulations it is shown that the proposed estimator achieves the bound for medium and large sample-sizes.
A problem that frequently occurs in biological experiments with laboratory animals is that some subjects are less susceptible to the treatment group than others. Finite mixture models have traditionally been used to d...
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A problem that frequently occurs in biological experiments with laboratory animals is that some subjects are less susceptible to the treatment group than others. Finite mixture models have traditionally been used to describe the distribution of responses in treated subjects for such studies. In this paper, we first study the mixture normal model with multi-levels and multiple mixture sub-populations under each level, with particular attention being given to the model in which the proportions of susceptibility are related to dose levels, then we use em-algorithm to find the maximum likelihood estimators of model parameters. Our results are generalizations of the existing results. Finally, we illustrate realistic significance of the above extension based on a set of real dose-response data.
Dimensionally reduced model-based clustering methods are recently receiving a wide interest in statistics as a tool for performing simultaneously clustering and dimension reduction through one or more latent variables...
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Dimensionally reduced model-based clustering methods are recently receiving a wide interest in statistics as a tool for performing simultaneously clustering and dimension reduction through one or more latent variables. Among these, Mixtures of Factor Analyzers assume that, within each component, the data are generated according to a factor model, thus reducing the number of parameters on which the covariance matrices depend. In Factor Mixture Analysis clustering is performed through the factors of an ordinary factor analysis which are jointly modelled by a Gaussian mixture. The two approaches differ in genesis, parameterization and consequently clustering performance. In this work we propose a model which extends and combines them. The proposed Mixtures of Factor Mixture Analyzers provide a unified class of dimensionally reduced mixture models which includes the previous ones as special cases and could offer a powerful tool for modelling non-Gaussian latent variables.
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.
We discuss an interpretation of the mixture transition distribution (MTD) for discrete-valued time series which is based on a sequence of independent latent variables which are occasion-specific. We show that, by assu...
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We discuss an interpretation of the mixture transition distribution (MTD) for discrete-valued time series which is based on a sequence of independent latent variables which are occasion-specific. We show that, by assuming that this latent process follows a first order Markov Chain, MTD can be generalized in a sensible way. A class of models results which also includes the hidden Markov model (HMM). For these models we outline an emalgorithm for the maximum likelihood estimation which exploits recursions developed within the HMM literature. As an illustration, we provide an example based on the analysis of stock market data referred to different American countries.
In this paper, we discuss inferential aspects for the Grubbs model when the unknown quantity x (latent response) follows a skew-normal distribution, extending early results given in Arellano-Valle et al. (J Multivar A...
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In this paper, we discuss inferential aspects for the Grubbs model when the unknown quantity x (latent response) follows a skew-normal distribution, extending early results given in Arellano-Valle et al. (J Multivar Anal 96:265-281, 2005b). Maximum likelihood parameter estimates are computed via the em-algorithm. Wald and likelihood ratio type statistics are used for hypothesis testing and we explain the apparent failure of the Wald statistics in detecting skewness via the profile likelihood function. The results and methods developed in this paper are illustrated with a numerical example.
In this article, we present the em-algorithm for performing maximum likelihood estimation of an asymmetric linear calibration model with the assumption of skew-normally distributed error. A simulation study is conduct...
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In this article, we present the em-algorithm for performing maximum likelihood estimation of an asymmetric linear calibration model with the assumption of skew-normally distributed error. A simulation study is conducted for evaluating the performance of the calibration estimator with interpolation and extrapolation situations. As one application in a real data set, we fitted the model studied in a dimensional measurement method used for calculating the testicular volume through a caliper and its calibration by using ultrasonography as the standard method. By applying this methodology, we do not need to transform the variables to have symmetrical errors. Another interesting aspect of the approach is that the developed transformation to make the information matrix nonsingular, when the skewness parameter is near zero, leaves the parameter of interest unchanged. Model fitting is implemented and the best choice between the usual calibration model and the model proposed in this article was evaluated by developing the Akaike information criterion, Schwarz's Bayesian information criterion and Hannan-Quinn criterion.
In this paper we have discussed inference aspects of the skew-normal nonlinear regression models following both, a classical and Bayesian approach, extending the usual normal nonlinear regression models. The univariat...
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In this paper we have discussed inference aspects of the skew-normal nonlinear regression models following both, a classical and Bayesian approach, extending the usual normal nonlinear regression models. The univariate skew-normal distribution that will be used in this work was introduced by Sahu et al. (Can J Stat 29:129-150, 2003), which is attractive because estimation of the skewness parameter does not present the same degree of difficulty as in the case with Azzalini (Scand J Stat 12:171-178, 1985) one and, moreover, it allows easy implementation of the em-algorithm. As illustration of the proposed methodology, we consider a data set previously analyzed in the literature under normality.
This paper gives a model of customer choice behavior modeling based on a combination of decision-making processes by applying latent class model based on emalgorithm. This model can apply for the choice problems of m...
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ISBN:
(纸本)9789898111111
This paper gives a model of customer choice behavior modeling based on a combination of decision-making processes by applying latent class model based on emalgorithm. This model can apply for the choice problems of multi services and multi brands under various decision-making processes. In addition to the model based on emalgorithm, we tried some conventional models and compared them. The model based on emalgorithm enables us to know what kinds of customers are classified into a certain class. Moreover, we could construct more accuracy model than conventional model and found the existence of two decision-making processes.
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