Minimum Hellinger distance estimation for Poisson mixtures

Karlis, Dimitris; Xekalaki, Evdokia

doi:10.1016/s0167-9473(98)00047-4

Cited by 33 publications

(22 citation statements)

References 22 publications

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“…Other problems arising in discrete-valued time series modeling with the proposed model are currently being studied, for example, parameter estimation by minimum Hellinger distance estimation (Karlis and Xekalaki 1998) and further consideration of other marginal probabilities such as binomial which will be of interest. Similar developments have been carried out by McKenzie (1987) and Weiß (2009).…”

Section: Discussionmentioning

confidence: 99%

Modeling time series of counts with a new class of INAR(1) model

2015

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This paper presents a new model for a stationary non-negative first order of integer-valued random variables based on the Pegram and thinning operators. Some fundamental and regression properties of the proposed model are discussed. Maximum likelihood estimation (MLE) by the EM algorithm is applied to estimate the parameters. Numerical studies to compare the proposed model with the thinning and Pegram models and the breakdown point of MLE for the proposed model have been conducted. Finally, a real life count data set has been used to illustrate its application. Comparison with existing models by AIC showed that the proposed model is much better and illustrates its potential usefulness in empirical modeling.

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Section: Discussionmentioning

confidence: 99%

Modeling time series of counts with a new class of INAR(1) model

2015

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“…Other problems arising in discrete-valued time series modelling by the proposed model are currently being studied, for example, parameter estimation by Minimum Hellinger Distance estimation [16] and consideration of other marginal probabilities such as binomial and negative binomial. See similar developments that have been carried out by Wei [17] and McKenzie [18].…”

Section: Discussionmentioning

confidence: 99%

A new model for time series of counts

Khoo¹,

Ong²

2014

AIP Conference Proceedings

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Time series modelling is an active research area in the past few decades with much attention focused in the continuous setting. However, time series data in terms of correlated counts occur in many situations. Thus modelling of time series of count data has attracted the attention many researchers recently. A new univariate non-negative stationary time series model of count data is introduced and is referred to as the mixture of Pegram and thinning on first order integer-valued autoregressive (MPT(1)) process. It is constructed from the combination of the popular thinning and Pegram's operators. The motivation for introducing the model and important statistical properties are discussed, such as autocorrelation, regression and joint distribution. Some simulation results are presented to show the performance of the model. Finally, the advantage of this new model is illustrated with application to a real data set.

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Section: Computational Detailsmentioning

confidence: 99%

“…The L 2 E objective function in Equation (5) is much simpler for computation than that of the MHDE, which is an extension of the HELMIX algorithm of [16]. As a result, the MDHE method is slower and more sensitive to the choice of initial values [16] than the L 2 E method. Also, as mentioned in Section 3, the L 2 E can be readily extended to the continuous response case and the key integral in the objective function has a closed form for many known mixtures, whereas the MHDE method for the continuous case would need conditional density estimators and optimal bandwidths, which place a severe burden on computations.…”

Section: Computational Detailsmentioning

confidence: 99%

On the performance ofL₂Eestimation in modelling heterogeneous count responses with extreme values

Lee

Sriram

2012

Journal of Statistical Computation and Simulation

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In healthcare studies, count data sets measured with covariates often exhibit heterogeneity and contain extreme values. To analyse such count data sets, we use a finite mixture of regression model framework and investigate a robust estimation approach, called the L 2 E [D.W. Scott, On fitting and adapting of density estimates, Comput. Sci. Stat. 30 (1998), pp. 124-133], to estimate the parameters. The L 2 E is based on an integrated L 2 distance between parametric conditional and true conditional mass functions. In addition to studying the theoretical properties of the L 2 E estimator, we compare the performance of L 2 E with the maximum likelihood (ML) estimator and a minimum Hellinger distance (MHD) estimator via Monte Carlo simulations for correctly specified and gross-error contaminated mixture of Poisson regression models. These show that the L 2 E is a viable robust alternative to the ML and MHD estimators. More importantly, we use the L 2 E to perform a comprehensive analysis of a Western Australia hospital inpatient obstetrical length of stay (LOS) (in days) data that contains extreme values. It is shown that the L 2 E provides a two-component Poisson mixture regression fit to the LOS data which is better than those based on the ML and MHD estimators. The L 2 E fit identifies admission type as a significant covariate that profiles the predominant subpopulation of normal-stayers as planned patients and the small subpopulation of long-stayers as emergency patients.

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Minimum Hellinger distance estimation for Poisson mixtures

Cited by 33 publications

References 22 publications

Modeling time series of counts with a new class of INAR(1) model

Modeling time series of counts with a new class of INAR(1) model

A new model for time series of counts

On the performance ofL₂Eestimation in modelling heterogeneous count responses with extreme values

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Minimum Hellinger distance estimation for Poisson mixtures

Cited by 33 publications

References 22 publications

Modeling time series of counts with a new class of INAR(1) model

Modeling time series of counts with a new class of INAR(1) model

A new model for time series of counts

On the performance ofL2Eestimation in modelling heterogeneous count responses with extreme values

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On the performance ofL₂Eestimation in modelling heterogeneous count responses with extreme values