Helmy, N., Shaaban, B., Elgohary, M. (2021). Robust Mixture Regression Estimation Based on least trimmed sum of absolute Method by using Several Models. test, 26(1), 50-72. doi: 10.21608/jsfc.2021.248605
Nahed Helmy; Batool Shaaban; Mervat Elgohary. "Robust Mixture Regression Estimation Based on least trimmed sum of absolute Method by using Several Models". test, 26, 1, 2021, 50-72. doi: 10.21608/jsfc.2021.248605
Helmy, N., Shaaban, B., Elgohary, M. (2021). 'Robust Mixture Regression Estimation Based on least trimmed sum of absolute Method by using Several Models', test, 26(1), pp. 50-72. doi: 10.21608/jsfc.2021.248605
Helmy, N., Shaaban, B., Elgohary, M. Robust Mixture Regression Estimation Based on least trimmed sum of absolute Method by using Several Models. test, 2021; 26(1): 50-72. doi: 10.21608/jsfc.2021.248605

Robust Mixture Regression Estimation Based on least trimmed sum of absolute Method by using Several Models

المجلة العلمية لقطاع کليات التجارة بجامعة الأزهر
Article 4, Volume 26, Issue 1, June 2021, Pages 50-72    PDF (9.27 M)
Document Type: المقالة الأصلية
DOI: 10.21608/jsfc.2021.248605
Authors
Nahed Helmy* 1; Batool Shaaban* 2; Mervat Elgohary2
1Al- Azhar Universit Faculty of Commerce - Girls' Branch Department of Statistics
2Al- Azhar Universit Faculty of Commerce - Girls' Branch Department of Statistics.
Abstract
The present study deals with one of the most important methods of the robust mixture regression estimators,least trimmed sum of absolute deviations LTA method. It is known that mixture regression models are used to investigate the relationship between variables that come from unknown latent groups and to model heterogenous datasets. In general, the error terms are assumed to be normal in the mixture regression model. However, the estimators under normality assumption are sensitive to the outliers. Therefore, we introduce a robust mixture regression procedure based on the LTA-estimation method to combat with the outliers in the data. In this paper, we handle LTA method by using three mixture regression models; Laplace, and normal distributions. We give a simulation study to illustrate the performance of the proposed estimators over the counterparts in terms of dealing with outliers. 
Keywords
EM algorithm; LTA-estimation method; Mixture regression model; Robust regression
References
  1. Agulló, J., Croux, C., and Van Aelst, S. (2008). “The multivariate Least-Trimmed Squares Estimator,” Journal of Multivariate Analysis, Vol. 99, pp. 311–338.
 

  1. Andrews, D.F. and Mallows, C.L. (1974). “Scale Mixtures of Normal Distributions”, Journal of the Royal Statistical Society. (B), Vol. 36, pp. 99-102.
 

  1. Bassett, G.W. (1991). “Equivariant, Monotonic, 50% Breakdown Estimators,” The American Statistician, Vol. 45, pp. 135-137.
 

  1. Chen, J., Tan, X., and Zhang, R. (2008). “Inference for Normal Mixture in Mean and Variance,” Statistica Sincia, Vol. 18, pp. 443-465.
 

  1. Croux, C., Rousseeuw, P.J., and Van Bael, A. (1996). “Positive-Breakdown Regression by Minimizing Nested Scale Estimators,” Journal of Statistical Planning and Inference, Vol. 53, pp. 197-235.

 

  1. Dias, J. G.,Wedel, M. (2004). An empirical comparison of EM, SEM and MCMC performance for problematic Gaussian mixture likelihoods. Statistics and Computing 14:323–332.
 

  1. Doğru, F.Z. and Arslan, O. (2017). “Robust Mixture Regression Modeling using the Least Trimmed Squares (LTS)-Estimation Method,” Article in Communication in Statistics- Simulation and Computation, Vol. 0, pp. 1-13.
 

  1. Hathaway, R. J. (1985). “A Constrained Formulation of Maximum-Likelihood Estimation for Normal Mixture Distributions,” Annals of Statistics, Vol. 13, pp. 795-800.
 

  1. Hathaway, R. J. (1986). “A Constrained EM Algorithm for Univariate Mixtures,” Journal of Statistical Computation and Simulation, Vol. 23, pp. 211-230.
 

  1. Hawkins, M.D. and Olive, D. (1999). “Applications and Algorithms for Least Trimmed Sum of Absolute Deviations Regression,” Southern IllinoisUniversityCarbondale, Articles and Preprints, Department of Mathematics, Computational Statistics and Data Analysis, Vol. 32, pp. 119-134
 

  1. H¨ossjer, O. (1991). “Rank-Based Estimates in the Linear Model with High Breakdown Point,” Ph.D. Thesis, Report 1991:5, Department of Mathematics, Uppsala University, Uppsala, Sweden.
 

  1. H¨ossjer, O. (1994). “Rank-Based Estimates in the Linear Model with High Breakdown Point,” Journal of the American Statistical Association, Vol. 89, pp. 149-158.

 

  1. Neykov, N., Filzmoser, P., Dimova, R., and Neytchev, P. (2007). “Robust fitting of mixtures using the trimmed likelihood estimator,”. Computational Statistics and Data Analysis, 52, 299-308.
 

  1. Phillips, R.F. (2002). “Least Absolute Deviations Estimation Via the EM Algorithm,” Statistics and Computing, Vol. 12, pp. 281-285.
 

15.   Song, W., Yao, W. and Xing, Y. (2014). “Robust Mixture Regression Model Fitting By Laplace Distribution,” Computational Statistics and Data Analysis,Vol. 71, pp. 128-137.

 

 

  1. Tableman, M. (1994a). “The Influence Functions for the Least Trimmed Squares and the Least Trimmed Absolute Deviations Estimators,” Statistics and Probability Letters, Vol. 19, pp. 329-337.

 

  1. Tableman, M. (1994b). “The Asymptotics of the Least Trimmed Absolute Deviations (LTAD) Estimator,” Statistics and Probability Letters, Vol. 19, pp. 387-398.

 

  1. Wei, Y. (2012). “Robust Mixture Regression Models Using T-Distribution” Master of Science Department of Statistics College of Arts and Sciences, Kansas State University Manhattan, Kansas.
 

  1. Yao, W. (2010). “A profile Likelihood Method for Normal Mixture with Unequal Variance,” Journal of Statistical Planning and Inference, Vol.140, pp. 2089-2098.
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