Maximum likelihood estimation of heterogeneous mixtures of Gaussian and uniform distributions

Coretto, Pietro; Hennig, Christian

doi:10.1016/j.jspi.2010.06.024

Cited by 45 publications

(24 citation statements)

References 37 publications

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“…Since a varying vector g implies different random variables in the mixture being analyzed, the extension of the study to this case is rather complex and remains an open issue to further investigate. Perhaps, in order to solve the open issues, the problem should be approached by a different perspective, following, for example, the works of Allman et al [7] and Coretto and Hennig [8,9], where the problem is studied from a general point of view and with reference to wide classes of mixture distributions or resorting to some non-classical definition of identifiability.…”

Section: Discussionmentioning

confidence: 99%

“…To our best knowledge, there is no general result for the identifiability of such a mixture in the literature, so far. Coretto and Hennig [8,9] proved the conditions for the identifiability of mixtures of Uniform random variables with any identifiable family of distributions with absolutely continuous cumulative density function, but no similar results have been obtained for the discrete case. So, we can resort to the method described in Section 2.…”

Section: Identifiability Of Nlcub Modelsmentioning

confidence: 99%

“…In the literature, there exist some results on the identifiability of mixture distributions, starting from the seminal works by Teicher [1] and Yakowitz and Spragins [2] who investigated identifiability for large families of finite mixtures. Further results have then been derived by Chandra [3], AlHussaini and Ahmad [4] and, more recently, McLachlan and Peel [5], Atienza et al [6], Allman et al [7] and Coretto and Hennig [8,9]. However these results, although being valid for a wide set of possible finite mixtures (e.g.…”

Section: Introductionmentioning

confidence: 95%

See 2 more Smart Citations

Identifiability of a model for discrete frequency distributions with a multidimensional parameter space

Manisera

Zuccolotto

2015

Journal of Multivariate Analysis

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This paper is concerned with the identifiability of models depending on a multidimensional parameter vector, aimed at fitting a probability distribution to discrete observed data, with a special focus on a recently proposed mixture model. Starting from the necessary and sufficient condition derived by the definition of identifiability, we describe a general method to verify whether a specific model is identifiable or not. This procedure is then applied to investigate the identifiability of a recently proposed mixture model for rating data, Nonlinear CUB, which is an extension of a class of mixture models called CUB (Combination of Uniform and Binomial).\ud Formal proofs and a numerical study show that some sufficient conditions for identifiability of Nonlinear CUB are always satisfied, provided that in the estimation procedure one quantity is fixed at a relatively small value

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Section: Discussionmentioning

confidence: 99%

Section: Identifiability Of Nlcub Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 95%

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Identifiability of a model for discrete frequency distributions with a multidimensional parameter space

Manisera

Zuccolotto

2015

Journal of Multivariate Analysis

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“…In fact, these observed abnormal realized volatility typically have an extremely scattered behavior not consistent with the main clusters referred as "regular clusters" in this work. The robust model-based clustering algorithm is based on the contribution of Banfield and Raftery (1993) and Coretto and Hennig (2011). The novelty here is that the aforementioned contributions are extended including constraints that ensures the desired separation between "regular" clusters, and (outlying) clusters representing abnormal volatility.…”

Section: Introductionmentioning

confidence: 99%

Improving Many Volatility Forecasts Using Cross-Sectional Volatility Clusters

Coretto

Rocca

Storti

2020

JRFM

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The inhomogeneity of the cross-sectional distribution of realized assets’ volatility is explored and used to build a novel class of GARCH (Generalized Autoregressive Conditional Heteroskedasticity) models. The inhomogeneity of the cross-sectional distribution of realized volatility is captured by a finite Gaussian mixture model plus a uniform component that represents abnormal variations in volatility. Based on the cross-sectional mixture model, at each time point, memberships of assets to risk groups are retrieved via maximum likelihood estimation, as well as the probability that an asset belongs to a specific risk group. The latter is profitably used for specifying a state-dependent model for volatility forecasting. We propose novel GARCH-type specifications the parameters of which act “clusterwise” conditional on past information on the volatility clusters. The empirical performance of the proposed models is assessed by means of an application to a panel of U.S. stocks traded on the NYSE. An extensive forecasting experiment shows that, when the main goal is to improve overall many univariate volatility forecasts, the method proposed in this paper has some advantages bover the state-of-the-arts methods.

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“…Banfield and Raftery (1993), Hennig (2004), and Coretto and Hennig (2011) propose methods to identify a noise component, while simultaneously clustering the non-noise observations. Banfield and Raftery model the noise component with a Poisson process and focus on robust estimation of cluster parameters.…”

Section: Introductionmentioning

confidence: 99%

Outlier Identification in Model-Based Cluster Analysis

Evans¹,

Love

Thurston

2015

J Classif

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In model-based clustering based on normal-mixture models, a few outlying observations can influence the cluster structure and number. This paper develops a method to identify these, however it does not attempt to identify clusters amidst a large field of noisy observations. We identify outliers as those observations in a cluster with minimal membership proportion or for which the cluster-specific variance with and without the observation is very different. Results from a simulation study demonstrate the ability of our method to detect true outliers without falsely identifying many non-outliers and improved performance over other approaches, under most scenarios. We use the contributed R package MCLUST for model-based clustering, but propose a modified prior for the cluster-specific variance which avoids degeneracies in estimation procedures. We also compare results from our outlier method to published results on National Hockey League data.

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Maximum likelihood estimation of heterogeneous mixtures of Gaussian and uniform distributions

Cited by 45 publications

References 37 publications

Identifiability of a model for discrete frequency distributions with a multidimensional parameter space

Identifiability of a model for discrete frequency distributions with a multidimensional parameter space

Improving Many Volatility Forecasts Using Cross-Sectional Volatility Clusters

Outlier Identification in Model-Based Cluster Analysis

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