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Articles

Variable selection in finite mixture of median regression models using skew-normal distribution

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Pages 30-48 | Received 18 Apr 2021, Accepted 25 Jul 2022, Published online: 06 Aug 2022

References

  • Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. International Symposium on Information Theory, 1, 610–624. https://doi.org/10.1007/978-1-4612-1694-0_15
  • Atienza, N., Garcia-Heras, J., & Muñoz-Pichardo, J. (2006). A new condition for identifiability of finite mixture distributions. Metrika, 63(2), 215–221. https://doi.org/10.1007/s00184-005-0013-z
  • Azzalini, A. (1985). A class of distributions which includes the normal ones. Scandinavian Journal of Statistics, 12(2), 171–178. http://www.jstor.org/stable/4615982
  • Azzalini, A., & Capitanio, A. (2013). The skew-normal and related families. Cambridge University Press.
  • Chen, J. (2017). Consistency of the MLE under mixture models. Statistical Science, 32(1), 47–63. https://doi.org/10.1214/16-sts578
  • Chen, J., Li, P., & Liu, G. (2020). Homogeneity testing under finite location-scale mixtures. Canadian Journal of Statistics, 48(4), 670–684. https://doi.org/10.1002/cjs.11557
  • Chen, J., & Tan, X. (2009). Inference for multivariate normal mixtures. Journal of Multivariate Analysis, 100(7), 1367–1383. https://doi.org/10.1016/j.jmva.2008.12.005
  • Cook, R.-D., & Weisberg, S. (1994). An introduction to regression graphics. John Wiley and Sons.
  • Fan, J., & Li, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statistical Association, 96(456), 1348–1360. https://doi.org/10.1198/016214501753382273
  • Goldfeld, S., & Quandt, R. (1973). A Markov model for switching regressions. Journal of Econometrics, 1(1), 3–15. https://doi.org/10.1016/0304-4076(73)90002-X
  • He, M., & Chen, J. (2022a). Consistency of the MLE under a two-parameter gamma mixture model with a structural shape parameter. Metrika. https://doi.org/10.1007/s00184-021-00856-9
  • He, M., & Chen, J. (2022b). Strong consistency of the MLE under two-parameter gamma mixture models with a structural scale parameter. Advances in Data Analysis and Classification, 16(1), 125–154. https://doi.org/10.1007/s11634-021-00472-5
  • Hu, D., Gu, Y., & Zhao, W. (2019). Bayesian variable selection for median regression. Chinese Journal of Applied Probability and Statistics, 35(6), 594–610.
  • Karlis, D., & Xekalaki, E. (2003). Choosing initial values for the EM algorithm for finite mixtures. Computational Statistics & Data Analysis, 41(3–4), 577–590. https://doi.org/10.1016/S0167-9473(02)00177-9
  • Khalili, A., & Chen, J. (2007). Variable selection in finite mixture of regression models. Journal of the American Statistical Association, 102(479), 1025–1038. https://doi.org/10.1198/016214507000000590
  • Kottas, A., & Gelfand, A. (2001). Bayesian semiparametric median regression modeling. Journal of the American Statistical Association, 96(456), 1458–1468. https://doi.org/10.1198/016214501753382363
  • Li, H., Wu, L., & Ma, T. (2017). Variable selection in joint location, scale and skewness models of the skew-normal distribution. Journal of Systems Science and Complexity, 30(3), 694–709. https://doi.org/10.1007/S11424-016-5193-2
  • Li, H., Wu, L., & Yi, J. (2016). A skew-normal mixture of joint location, scale and skewness models. Applied Mathematics-A Journal of Chinese Universities, 31(3), 283–295. https://doi.org/10.1007/S11766-016-3367-2
  • Li, J., Ray, S., & Lindsay, B.-G. (2007). A nonparametric statistical approach to clustering via mode identification. Journal of Machine Learning Research, 8(8), 1687–1723.
  • Lin, T.-I., Lee, J., & Yen, S. (2007). Finite mixture modelling using the skew normal distribution. Statistica Sinica, 17(3), 909–927. http://www.jstor.org/stable/24307705
  • Liu, M., & Lin, T.-I. (2014). A skew-normal mixture regression model. Educational and Psychological Measurement, 74(1), 139–162. https://doi.org/10.1177/0013164413498603
  • McLachlan, G., & Peel, D. (2004). Finite mixture models. John Wiley and Sons.
  • Otiniano, C. E. G., Rathie, P. N., & Ozelim, L. C. S. M. (2015). On the identifiability of finite mixture of skew-normal and skew-t distributions. Statistics & Probability Letters, 106, 103–108. https://doi.org/10.1016/j.spl.2015.07.015
  • Richardson, S., & Green, P. (1997). On bayesian analysis of mixtures with an unknown number of components (with discussion). Journal of the Royal Statistical Society: Series B (Statistical Methodology), 59(4), 731–792. https://doi.org/10.1111/1467-9868.00095
  • Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6(2), 461–464. https://doi.org/10.1214/AOS/1176344136
  • Tang, A., & Tang, N. (2015). Semiparametric Bayesian inference on skew-normal joint modeling of multivariate longitudinal and survival data. Statistics in Medicine, 34(5), 824–843. https://doi.org/10.1002/SIM.6373
  • Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society. Series B. Statistical Methodology, 58(1), 267–288. https://doi.org/10.1111/J.2517-6161.1996.TB02080.X
  • Titterington, D., Smith, A., & Makov, U. (1985). Statistical analysis of finite mixture distributions. John Wiley and Sons
  • Wang, H., Li, R., & Tsai, C. (2007). Tuning parameter selectors for the smoothly clipped absolute deviation method. Biometrika, 94(3), 553–568. https://doi.org/10.1093/BIOMET/ASM053
  • Wang, P., Puterman, M., Cockburn, I., & Le, N. (1996). Mixed Poisson regression models with covariate dependent rates. Biometrics, 52(2), 381–400. https://doi.org/10.2307/2532881
  • Wu, L. (2014). Variable selection in joint location and scale models of the skew-t-normal distribution. Communications in Statistics. Simulation and Computation, 43(3), 615–630. https://doi.org/10.1080/03610918.2012.712182
  • Wu, L., Li, S., & Tao, Y. (2020). Estimation and variable selection for mixture of joint mean and variance models. Communications in Statistics-Theory and Methods, 50(24), 6081–6098. https://doi.org/10.1080/03610926.2020.1738493
  • Wu, L., Zhang, Z., & Xu, D. (2013). Variable selection in joint location and scale models of the skew-normal distribution. Journal of Statistical Computation and Simulation, 83(7), 1266–1278. https://doi.org/10.1080/00949655.2012.657198
  • Yao, W., & Li, L. (2014). A new regression model: Modal linear regression. Scandinavian Journal of Statistics, 41(3), 656–671. https://doi.org/10.1111/SJOS.12054
  • Yin, J., Wu, L., & Dai, L. (2020). Variable selection in finite mixture of regression models using the skew-normal distribution. Journal of Applied Statistics, 47(16), 2941–2960. https://doi.org/10.1080/02664763.2019.1709051
  • Yin, J., Wu, L., Lu, H., & Dai, L. (2020). New estimation in mixture of experts models using the Pearson type VII distribution. Communications in Statistics. Simulation and Computation, 49(2), 472–483. https://doi.org/10.1080/03610918.2018.1485943
  • Zhou, X., & Liu, G. (2016). LAD-Lasso variable selection for doubly censored median regression models. Communications in Statistics. Theory and Methods, 45(12), 3658–3667. https://doi.org/10.1080/03610926.2014.904357