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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2016 / Cilt: 45 - Sayı: 2

Robust variable selection for mixture linear regression models

Yunlu Jiang
Sayfa
549–559
Yayın Tarihi
2022-10-18
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Finally, we apply the proposed methodology to analyze a real data.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper, we propose a robust variable selection to estimate and select relevant covariates for the finite mixture of linear regression models by assuming that the error terms follow a Laplace distribution to the data after trimming the high leverage points.
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Temel Bulgular & Veri:We introduce a revised Expectation-maximization (EM) algorithm for numerical computation.
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Sonuç & Katkı:Finally, we apply the proposed methodology to analyze a real data.
🔬Tür:Modelleme & Sayısal Simülasyon
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Finite mixture of linear regression models · Robustness · EM-algorithm

Abstract

In this paper, we propose a robust variable selection to estimate and select relevant covariates for the finite mixture of linear regression models by assuming that the error terms follow a Laplace distribution to the data after trimming the high leverage points. We introduce a revised Expectation-maximization (EM) algorithm for numerical computation. Simulation studies indicate that the proposed method is robust to both the high leverage points and outliers in the y-direction, and can obtain a consistent variable selection in the case of outliers or heavy-tail error distribution. Finally, we apply the proposed methodology to analyze a real data.

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Bu Makaleye Atıf Yap

Jiang, Y. (2022). Robust variable selection for mixture linear regression models. Hacettepe Journal of Mathematics and Statistics, Cilt: 45 - Sayı: 2, 549–559. https://ajindex.com/articles/530145

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Kaynakça (17)

  1. Bai, X., Yao, W., and Boyer, J. E. Robust fitting of mixture regression models, Comput. Stat. Data. An. 56 (7), 2347-2359, 2012.
  2. Croux, C., and Haesbroeck, G. Influence function and efficiency of the mini- mum covariance determinant scatter matrix estimator, J. Multivariate Anal. 71 (2), 161-190, 1999.
  3. Davies, P. Asymptotic Behaviour of S-Estimates of Multivariate Location Param- eters and Dispersion Matrices, Ann. Statist. 15 (3), 1269-1292, 1987.
  4. Donoho, D. L. Breakdown properties of multivariate location estimators„ Technical report, Technical report, Harvard University, Boston. URL http://www-stat. stanford. edu/ donoho/Reports/Oldies/BPMLE. pdf, 1982.
  5. Du, Y., Khalili, A., Neslehova, J. G., and Steele, R. J. Simultaneous fixed and random effects selection in finite mixture of linear mixed-effects models, Can. J. Stat. 41 (4), 596-616, 2013.
  6. Fan, J., and Li, R. Variable selection via nonconcave penalized likelihood and its oracle properties, J. Amer. Statist. Assoc. 96 (456), 1348-1360, 2001.
  7. Huang, M., Li, R., Wang, H., and Yao, W. Estimating Mixture of Gaussian Pro- cesses by Kernel Smoothing, J. Bus. Econ. Stat. 32 (2), 259-270, 2014.
  8. Huang, M., Li, R., and Wang, S. Nonparametric mixture of regression models, J. Amer. Statist. Assoc. 108 (503), 929-941, 2013.
  9. Huang, M., and Yao, W. Mixture of regression models with varying mixing pro- portions: a semiparametric approach, J. Amer. Statist. Assoc. 107 (498), 711-724, 2012.
  10. Hunter, D. R., and Li, R. Variable selection using MM algorithms, Ann. Statist. 33 (4), 1617-1642, 2005.
  11. Hunter, D. R., and Young, D. S. Semiparametric mixtures of regressions, J. Nonparametr. Stat. 24 (1), 19-38, 2012.
  12. Jacobs, R. A., Jordan, M. I., Nowlan, S. J., and Hinton, G. E. Adaptive mixtures of local experts, Neural. Comput. 3 (1), 79-87, 1991.
  13. Jiang, W., Tanner, M. A. et al. Hierarchical mixtures-of-experts for exponential fam- ily regression models: approximation and maximum likelihood estimation, Ann. Statist. 27 (3), 987-1011, 1997.
  14. Khalili, A. An Overview of the New Feature Selection Methods in Finite Mixture of Regression Models, J. Iran. Stat. Soc. 10 (2), 201-235, 2011.
  15. Khalili, A., and Chen, J. Variable Selection in Finite Mixture of Regression Models, J. Amer. Statist. Assoc. 102 (479), 1025-1038, 2007.
  16. Khalili, A., and Lin, S. Regularization in finite mixture of regression models with diverging number of parameters, Biometrics 69 (2), 436-446, 2013.
  17. Luo, R., Wang, H., and Tsai, C.-L.On Mixture Regression Shrinkage