- Volume 26 Issue 4
DOI QR Code
A numerical study on group quantile regression models
- Kim, Doyoen (Department of Statistics, Korea University) ;
- Jung, Yoonsuh (Department of Statistics, Korea University)
- Received : 2019.01.02
- Accepted : 2019.06.14
- Published : 2019.07.31
Grouping structures in covariates are often ignored in regression models. Recent statistical developments considering grouping structure shows clear advantages; however, reflecting the grouping structure on the quantile regression model has been relatively rare in the literature. Treating the grouping structure is usually conducted by employing a group penalty. In this work, we explore the idea of group penalty to the quantile regression models. The grouping structure is assumed to be known, which is commonly true for some cases. For example, group of dummy variables transformed from one categorical variable can be regarded as one group of covariates. We examine the group quantile regression models via two real data analyses and simulation studies that reveal the beneficial performance of group quantile regression models to the non-group version methods if there exists grouping structures among variables.
Supported by : National Research Foundation of Korea
- Bakin S (1999). Adaptive regression and model selection in data mining problems (PhD thesis), The Australian National University.
- Chavent M and Kuentz-Simonet V (2012). ClustOfVar: an R package for the clustering of variables, Journal of Statistical Software, 50, 1-16.
- Ciuperca G (2019). Adaptive group LASSO selection in quantile models, Statistical Papers, 60, 173-197. https://doi.org/10.1007/s00362-016-0832-1
- Fan J (1997). Comments on wavelets in statistics: a review by A. Antoniadis, Journal of the Italian Statistical Society, 6, 131-138. https://doi.org/10.1007/BF03178906
- 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
- Hashem H, Vinciotti V, Alhamzawi R, and Yu K (2016). Quantile regression with group lasso for classification, Advances in Data Analysis and Classification, 10, 375-390. https://doi.org/10.1007/s11634-015-0206-x
- Hendricks W and Koenker R (1992). Hierarchical spline models for conditional quantiles and the demand for electricity, Journal of the American Statistical Association, 87, 58-68. https://doi.org/10.1080/01621459.1992.10475175
- Hoerl AE and Kennard RW (1970). Ridge regression: biased estimation for nonorthogonal problems, Technometrics, 12, 55-67. https://doi.org/10.1080/00401706.1970.10488634
- Hosmer DW and Lemeshow S (1989). Applied logistic regression, Wiley, Vol. 2.
- Huang J, Breheny P, and Ma S (2012). A Selective Review of Group Selection in High-Dimensional Models, Statistical Science, 27, 481-499. https://doi.org/10.1214/12-STS392
- Kato K (2011). Group Lasso for high dimensional sparse quantile regression models, arXiv:1103.1458 v2 [stat.ME].
- Koenker R (2004). Quantile regression for longitudinal data, Journal of Multivariate Analysis, 91, 74-89. https://doi.org/10.1016/j.jmva.2004.05.006
- Koenker R and Bassett G (1978). Regression quantiles, Econometrica, 46, 33-50. https://doi.org/10.2307/1913643
- Koenker R and Hallock KF (2001). Quantile regression, Journal of Economic Perspectives, 15, 143-156. https://doi.org/10.1257/jep.15.4.143
- Koenker R, NG P, and Portnoy S (1994). Quantile smoothing splines, Biometrika, 81, 673-680. https://doi.org/10.1093/biomet/81.4.673
- Ogutu JO and Piepho HP (2014). Regularized group regression methods for genomic prediction: Bridge, MCP, SCAD, group bridge, group lasso, sparse group lasso, group MCP and group SCAD, BMC Proceedings, 8.
- Sakar BE, Isenkul ME, Sakar CO, Sertbas A, Gurgen F, Delil S, Apaydin H, and Kursun O (2013). Collection and analysis of a Parkinson Speech Dataset with multiple types of sound recordings, IEEE Journal of Biomedical and Health Informatics, 17, 828-834. https://doi.org/10.1109/JBHI.2013.2245674
- Tibshirani R (1996). Regression shrinkage and selection via the lasso, Journal of the Royal Statistical Society. Series B (Methodological), 58, 267-288. https://doi.org/10.1111/j.2517-6161.1996.tb02080.x
- Wang H and He X (2007). Detecting differential expressions in GeneChip microarray studies: a quantile approach, Journal of the American Statistical Association, 102, 104-112. https://doi.org/10.1198/016214506000001220
- Wei Y and He X (2006). Conditional growth charts, The Annals of Statistics, 34, 2069-2097. https://doi.org/10.1214/009053606000000623
- Wei Y, Pere A, Koenker R, and He X (2006). Quantile regression methods for reference growth charts, Statistics in Medicine, 25, 1369-1382. https://doi.org/10.1002/sim.2271
- Wu Y and Liu Y (2009). Variable selection in quantile regression, Statistica Sinica, 19, 801-817.
- Yuan M and Lin Y (2006). Model selection and estimation in regression with grouped variables, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 68, 49-67. https://doi.org/10.1111/j.1467-9868.2005.00532.x
- Zhang CH (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
- Zou H and Hastie T (2005). Regularization and variable selection via the elastic net, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 67, 301-320. https://doi.org/10.1111/j.1467-9868.2005.00503.x