Abstract
We proposed a stochastic EM algorithm for quantile and censored quantile regression models in order to circumvent some limitations of the EM algorithm and Gibbs sampler. We conducted several simulation studies to illustrate the performance of the algorithm and found that the procedure performs as better as the Gibbs sampler, and outperforms the EM algorithm in uncensored situation. Finally we applied the methodology to the classical Engel food expenditure data and the labour supply data with left censoring, finding that the SEM algorithm behaves more satisfying than the Gibbs sampler does.
Similar content being viewed by others
References
Alhamzawi, R. (2016). Bayesian elastic net Tobit quantile regression. Communications in Statistics: Simulation and Computation, 45(7), 2409–2427.
Alhamzawi, R., & Yu, K. M. (2012). Variable selection in quantile regression via Gibbs sampling. Journal of Applied Statistics, 39(4), 799–813.
Alhamzawi, R., & Yu, K. M. (2015). Bayesian Tobit quantile regression using g-prior distribution with ridge parameter. Journal of Statistical Computation and Simulation, 85(14), 2903–2918.
Barndorff-Nielsen, O. E., & Shephard, N. (2001). Non-Gaussian Ornstein–Uhlenbeck-based models and some of their uses in financial economics. Journal of the Royal Statistical Society, Series B, 63(2), 167–241.
Celeux, G., Chauveau, D., & Diebolt, J. (1996). Stochastic versions of the EM algorithm: An experimental study in the mixture case. Journal of Statistical Computation and Simulation, 55(4), 287–314.
Celeux, G., & Diebolt, J. (1985). The SEM algorithm: A probabilistic teacher algorithm derived from the EM algorithm for the mixture problem. Computational Statistics Quarterly, 2, 73–82.
Diebolt, J., & Robert, C. P. (1994). Estimation of finite mixture distributions through Bayesian sampling. Journal of the Royal Statistical Society, Series B, 56(2), 363–375.
Ip, E. H. S.(1994). A stochastic EM estimator in the presence of missing data-theory and applications. Technical report, No. 304. Department of statistics, Stanford University, Stanford, California.
Ji, Y. G., Lin, N., & Zhang, B. X. (2012). Model selection in binary and tobit quantile regression using the Gibbs sampler. Computational Statistics & Data Analysis, 56(4), 827–839.
Koenker, R. (2005). Quantile regression. Cambridge: Cambridge University Press.
Koenker, R., & Bassett, G. (1978). Regression quantiles. Econometrica, 46(1), 33–50.
Kou, G., Peng, Y., & Wang, G. X. (2014). Evaluation of clustering algorithm for financial risk analysis using MCDM methods. Information Sciences, 275, 1–12.
Kozumi, H., & Kobayashi, G. (2011). Gibbs sampling methods for Bayesian quantile regression. Journal of Statistical Computation and Simulation, 81(11), 1565–1578.
Mroz, T. (1987). The sensitivity of an empirical model of married womens hours of work to economic and statistical assumptions. Econometrica, 55(4), 765–799.
Nielsen, S. F. (2000). The stochastic EM algorithm: Estimation and asymptotic results. Bernoulli, 6(3), 457–489.
Powell, J. (1986). Censored regression quantiles. Journal of Econometrics, 32(1), 143–155.
Reed, C. & Yu, K.(2009). A partially collapsed Gibbs sampler for Bayesian quantile regression. Technical report, Brunel University, UK.
Tian, Y. Z., Tian, M. Z., & Zhu, Q. Q. (2014). Linear quantile regression based on EM algorithm. Communications in Statistics: Theory and Methods, 43(16), 3464–3484.
Tian, Y. Z., Zhu, Q. Q., & Tian, M. Z. (2016). Estimation of linear composite quantile regression using EM algorithm. Statistics and Probability Letters, 117, 183–191.
Yu, K., & Stander, J. (2007). Bayesian analysis of a Tobit quantile regression model. Journal of Econometrics, 137(1), 260–276.
Yu, K., & Zhang, J. (2005). A three-parameter asymmetric Laplace distribution and its extension. Communications in Statistics: Theroy and Method, 4(9–10), 1867–1879.
Zhou, Y. H., Ni, Z. X., & Li, Y. (2014). Quantile regression via the EM algorithm. Communications in Statistics: Simulation and Computation, 43(10), 2162–2172.
Acknowledgements
The authors gratefully acknowledge the editor and referees for their valuable comments and suggestions.
Author information
Authors and Affiliations
Corresponding author
Additional information
This research is supported by The National Science Foundation of China Grants 11371227.
Rights and permissions
About this article
Cite this article
Yang, F. A Stochastic EM Algorithm for Quantile and Censored Quantile Regression Models. Comput Econ 52, 555–582 (2018). https://doi.org/10.1007/s10614-017-9704-6
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10614-017-9704-6