Estimating the mixing proportion in a semiparametric mixture model

Song, Seongjoo; Nicolae, Dan L.; Song, Jongwoo

doi:10.1016/j.csda.2010.04.007

Cited by 9 publications

(41 citation statements)

References 11 publications

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“…The symmetry method in [8] shares similar complexity 6 O(n 2 ). Last but not least, the EM-type method of [5] and their π−maximizing one have the advantage over other methods, because we need only to calculate a kernel density estimator once and for all, then use it at each iteration 7 . Nevertheless, the method has still a complexity of order n 2 .…”

Section: Simulation Studymentioning

confidence: 99%

“…The semiparametric model was employed in [4] (supposing that θ is known) for multiple testing procedures in order to estimate the posterior population probabilities and the local false rate discovery. In [5], the authors studied a similar setup where θ is unknown without further assumptions on f 0 . They applied the semiparametric model in sequential clustering algorithms as a second step after having calculated the centers of the clusters.…”

Section: Introductionmentioning

confidence: 99%

“…Besides, the authors prove (see also [1]) that the model becomes identifiable under further assumptions on the parametric component. Two other estimation methods were proposed in [5]; the π−maximizing method and an EMtype algorithm. The π−maximizing method is based on the identifiability of model (1) when f 1 is a scale Gaussian model.…”

Section: Introductionmentioning

confidence: 99%

“…A comparison between the three methods proposed in [8] and [5] is illustrated in [2] and are comparted to the Hellinger-based iterative method of the same authors on a two-component Gaussian data provided that the parametric component is fully known. As we add θ to the set of unknown parameters, i.e.…”

Section: Introductionmentioning

confidence: 99%

“…The difference between these methods is in their way of calculating the vector of weights. EM-type methods are not based on the minimization of a criterion function as in [8] or [5]. Besides, their asymptotic properties are generally very difficult to establish.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Semiparametric Two-Component Mixture Models When One Component Is Defined Through Linear Constraints

Mohamad¹,

Boumahdaf²

2018

IEEE Trans. Inform. Theory

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We propose a structure of a semiparametric two-component mixture model when one component is parametric and the other is defined through linear constraints on its distribution function. Estimation of a two-component mixture model with an unknown component is very difficult when no particular assumption is made on the structure of the unknown component. A symmetry assumption was used in the literature to simplify the estimation. Such method has the advantage of producing consistent and asymptotically normal estimators, and identifiability of the semiparametric mixture model becomes tractable. Still, existing methods which estimate a semiparametric mixture model have their limits when the parametric component has unknown parameters or the proportion of the parametric part is either very high or very low. We propose in this paper a method to incorporate a prior linear information about the distribution of the unknown component in order to better estimate the model when existing estimation methods fail. The new method is based on ϕ−divergences and has an original form since the minimization is carried over both arguments of the divergence. The resulting estimators are proved to be consistent and asymptotically normal under standard assumptions. We show that using the Pearson's χ 2 divergence our algorithm has a linear complexity when the constraints are moment-type. Simulations on univariate and multivariate mixtures demonstrate the viability and the interest of our novel approach.

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Section: Simulation Studymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Semiparametric Two-Component Mixture Models When One Component Is Defined Through Linear Constraints

Mohamad¹,

Boumahdaf²

2018

IEEE Trans. Inform. Theory

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Minimum profile Hellinger distance estimation for a semiparametric mixture model

Xiang

Yao

2014

Can J Statistics

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In this paper, we propose a new effective estimator for a class of semiparametric mixture models where one component has known distribution with possibly unknown parameters while the other component density and the mixing proportion are unknown. Such semiparametric mixture models have been often used in multiple hypothesis testing and the sequential clustering algorithm. The proposed estimator is based on the minimum profile Hellinger distance (MPHD), and its theoretical properties are investigated. In addition, we use simulation studies to illustrate the finite sample performance of the MPHD estimator and compare it with some other existing approaches. The empirical studies demonstrate that the new method outperforms existing estimators when data are generated under contamination and works comparably to existing estimators when data are not contaminated. Applications to two real data sets are also provided to illustrate the effectiveness of the new methodology. The Canadian Journal of Statistics 42: 246–267; 2014 © 2014 Statistical Society of Canada

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Semiparametric location mixtures with distinct components

Hohmann

Holzmann

2013

Statistics

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Estimating the mixing proportion in a semiparametric mixture model

Cited by 9 publications

References 11 publications

Semiparametric Two-Component Mixture Models When One Component Is Defined Through Linear Constraints

Semiparametric Two-Component Mixture Models When One Component Is Defined Through Linear Constraints

Minimum profile Hellinger distance estimation for a semiparametric mixture model

Semiparametric location mixtures with distinct components

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