Figure 4.1. Boxplot of estimated α.
Figure 4.2. Boxplot of estimated coefficients for SCAD-SCAD case with n = 500, ρ = 0.8.
Figure 4.3. Boxplot of estimated coefficients for SCAD-Adplasso case with n = 500, ρ = 0.8.
Figure 5.1. Histogram of salary (y) (a) and log(salary) (b).
Table 4.1. Frequencies and percents of number of components for ρ = 0.5 and K = 3
Table 4.2. C and IC of α and β (ρ = 0.5)
Table 4.3. Frequencies and percents of number of components for ρ = 0.8 and K = 3
Table 4.4. C and IC of α and β (ρ = 0.8)
Table 5.1. Coefficient estimates for various models (M: Mixture reg.)
Table 5.2. RMSEP and REP for various models (L: Linear reg., M: Mixture reg.)
참고문헌
- Akaike, H. (1973), Information theory and an extension of the maximum likelihood principle. In Second International Symposium on Information Theory, eds. Petrox, B. N., and Caski, F., Budapest: Akademiai Kiado, pp. 267.
- Breiman, L. (1996). Heuristics of instability and stabilization in model selection, The Annals of Statistics, 24, 2350-2383. https://doi.org/10.1214/aos/1032181158
- Chen, J. (1995). Optimal rate of convergence for finite mixture models, The Annals of Statistics, 23, 221-233. https://doi.org/10.1214/aos/1176324464
- Chen, J. and Khalili, A. (2008). Order selection in finite mixture models with a nonsmooth penalty, Journal of the American Statistical Association, 104, 187-196. https://doi.org/10.1198/jasa.2009.0103
- Dempster, A. P., Laird, N. M., and Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm (with discussion), Journal of the Royal Statistical Society, Series B, 39, 1-38.
- Fan, J. and Li, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties, Journal of the American Statistical Association, 96, 1348-1360. https://doi.org/10.1198/016214501753382273
- Fan, J. and Li, R. (2002). Variable selection for Cox's proportional hazards model and frailty model, The Annals of Statistics, 30, 74-99. https://doi.org/10.1214/aos/1015362185
- Hastings. W. (1970). Monte Carlo sampling methods using Markov Chains and their applications, Biometrika, 57, 97-109. https://doi.org/10.1093/biomet/57.1.97
- Huang, T., Peng, H. and Zhang, K. (2017). Model Selection for Gaussian mixture models, Statistica Sinica, 27, 147-169.
- Khalili, A. and Chen, J. (2007). Variable Selection in Finite Mixture of Regression Models, Journal of the American Statistical Association, 102, 1025-1038. https://doi.org/10.1198/016214507000000590
- Luo, R., Wang, H., and Tsai, C. (2008), On mixture regression shrinkage and selection via the MR-lasso, International Journal of Pure and Applied Mathematics, 46, 403-414.
- McLachlan, G. and D. Peel (2000). Finite Mixture Model, John Wiley & Sons, Inc.
- Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., and Teller, E. (1953). Equation of state calculations by fast computing machine, Journal of Chemical Physics, 21, 1087-1091. https://doi.org/10.1063/1.1699114
- Pearson, K. (1894). Contributions to the Mathematical Theory of Evolution, Philosophical Transactions of the Royal Society of London. A, 185, 71-110. https://doi.org/10.1098/rsta.1894.0003
- Schwarz, G. (1978). Estimating the dimension of a model, The Annals of Statistics, 6, 461-464. https://doi.org/10.1214/aos/1176344136
- Skrondal, A. and Rabe-Hesketh, S. (2004). Generalized Latent Variable Modelling: Multilevel, Longitudinal, and Structural Equation Models, Chapman & Hall/CRC, FL.
- Tibshirani, R. (1996). Regression shrinkage and selection via the lasso, Journal of the Royal Statistical Society. Series B, 58, 267-288.
- Wedel, M. and Kamakura, W. A. (2000). Market Segmentation: Conceptual and Methodological Foundations (2nd ed), Kluwer Academic Publishers, Boston.
- Zhang, C. (2010). Nearly unbiased variable selection under minimax concave penalty, The Annals of statistics, 38, 894-942. https://doi.org/10.1214/09-AOS729
- Zou, H. (2006). The adaptive lasso and its oracle properties, Journal of the American Statistical Association, 101, 1418-1429. https://doi.org/10.1198/016214506000000735