Robust Mixture of Linear Regression Models

Bashir, Shaheena; Carter, E. M.

doi:10.1080/03610926.2011.558655

Cited by 26 publications

(15 citation statements)

References 8 publications

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“…Robust estimation is commonly performed by resorting to a suitable modification of the EM (or the Classification EM, CEM hereafter) algorithm obtained by replacing the standard likelihood equations characterizing the M-step. For instance, robust estimation of mixtures can be achieved by using soft-trimming procedures based on M-type estimators (Bai et al 2012 ; Bashir and Carter 2012 ; Farcomeni and Greco 2015b ) or on weighted likelihood estimating equations (Markatou 2000 ; Greco and Agostinelli 2020 ; Greco et al 2020 ). According to this approach, the M-step is enhanced by the computation of data-dependent weights laying in [0, 1], aimed to bound the effect of anomalous observations.…”

Section: Introductionmentioning

confidence: 99%

Robust fitting of mixtures of GLMs by weighted likelihood

Greco

2021

AStA Adv Stat Anal

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Finite mixtures of generalized linear models are commonly fitted by maximum likelihood and the EM algorithm. The estimation process and subsequent inferential and classification procedures can be badly affected by the occurrence of outliers. Actually, contamination in the sample at hand may lead to severely biased fitted components and poor classification accuracy. In order to take into account the potential presence of outliers, a robust fitting strategy is proposed that is based on the weighted likelihood methodology. The technique exhibits a satisfactory behavior in terms of both fitting and classification accuracy, as confirmed by some numerical studies and real data examples.

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Section: Introductionmentioning

confidence: 99%

Robust fitting of mixtures of GLMs by weighted likelihood

Greco

2021

AStA Adv Stat Anal

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“…Bai et al () developed a modified EM algorithm by adopting a robust criterion in the M‐step. Bashir & Carter () extended the idea of the S‐estimator to mixture regression. Yu et al () proposed a robust mixture regression via mean‐shift penalisation approach to conduct simultaneous outlier detection and robust mixture model estimation.…”

Section: Introductionmentioning

confidence: 99%

A Selective Overview and Comparison of Robust Mixture Regression Estimators

Yao

Yang

2019

Int Statistical Rev

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Summary Mixture regression models have been widely used in business, marketing and social sciences to model mixed regression relationships arising from a clustered and thus heterogeneous population. The unknown mixture regression parameters are usually estimated by maximum likelihood estimators using the expectation–maximisation algorithm based on the normality assumption of component error density. However, it is well known that the normality‐based maximum likelihood estimation is very sensitive to outliers or heavy‐tailed error distributions. This paper aims to give a selective overview of the recently proposed robust mixture regression methods and compare their performance using simulation studies.

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“…We also parallel research on the estimation of mixture linear regressions. Bashir and Carter (2012) consider a model where there are k latent populations each satisfying a linear model Y k = X T k β k + k . Assuming that the errors k ∼ N (0, σ k ) are independent across populations, the authors provide an expectation maximization algorithm to recover the class labels, β k , and σ k .…”

Section: Introductionmentioning

confidence: 99%

Finding Exogenous Variation in Data

2018

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We reconsider the classic problem of recovering exogenous variation from an endogenous regressor. Two-stage least squares recovers exogenous variation through presuming the existence of an instrumental variable. We rely instead on the assumption that the regressor is a mixture of exogenous and endogenous observations-say as the result of temporary natural experiments. With this assumption, we propose an alternative two-stage method based on nonparametrically estimating a mixture model to recover a subset of the exogenous observations. We demonstrate that our method recovers exogenous observations in simulation and can be used to find pricing experiments hidden in grocery store scanner data.

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Robust Mixture of Linear Regression Models

Cited by 26 publications

References 8 publications

Robust fitting of mixtures of GLMs by weighted likelihood

Robust fitting of mixtures of GLMs by weighted likelihood

A Selective Overview and Comparison of Robust Mixture Regression Estimators

Finding Exogenous Variation in Data

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