An elastic-net penalized expectile regression with applications

References

• D.J. Aigner, T. Amemiya, and D.J. Poirier, On the estimation of production frontiers: maximum likelihood estimation of the parameters of a discontinuous density function, Int. Econ. Rev. (Philadelphia) 17 (1976), pp. 377–396. doi: 10.2307/2525708
   Google Scholar
• R. Alhamzawi, Conjugate priors and variable selection for bayesian quantile regression, Comput. Stat. Data Anal. 64 (2013), pp. 209–219. doi: 10.1016/j.csda.2012.01.014
   Web of Science ®Google Scholar
• R. Alhamzawi, K. Yu, and D.F. Benoit, Bayesian adaptive lasso quantile regression, Stat. Model. 12 (2012), pp. 279–297. doi: 10.1177/1471082X1101200304
   Web of Science ®Google Scholar
• T. Alshaybawee, R. Alhamzawi, H. Midi, and I.I. Allyas, Bayesian variable selection and coefficient estimation in heteroscedastic linear regression model, J. Appl. Stat. 45 (2018), pp. 2643–2657. doi: 10.1080/02664763.2018.1432576
   Web of Science ®Google Scholar
• T. Alshaybawee, H. Midi, and R. Alhamzawi, Bayesian elastic net single index quantile regression, J. Appl. Stat. 44 (2017), pp. 853–871. doi: 10.1080/02664763.2016.1189515
   Web of Science ®Google Scholar
• M. Amin, L. Song, M.A. Thorlie, and X. Wang, SCAD-penalized quantile regression for high-dimensional data analysis and variable selection, Stat. Neerl. 69 (2015), pp. 212–235. doi: 10.1111/stan.12056
   Web of Science ®Google Scholar
• F. Bellini, L. Mercuri, and E. Rroji, Implicit expectiles and measures of implied volatility, Quant. Finance. 18 (2018), pp. 1851–1864. doi: 10.1080/14697688.2018.1447680
   Web of Science ®Google Scholar
• A. Belloni and V. Chernozhukov, L1-penalized quantile regression in high-dimensional sparse models, Ann. Stat. 39 (2011), pp. 82–130. doi: 10.1214/10-AOS827
   Web of Science ®Google Scholar
• P. Breheny and J. Huang, Coordinate descent algorithms for nonconvex penalized regression, with applications to biological feature selection, Ann. Appl. Stat. 5 (2011), pp. 232–253. doi: 10.1214/10-AOAS388
   PubMed Web of Science ®Google Scholar
• L.F. Burgette, Exploratory quantile regression with many covariates an application to adverse birth outcomes, Epidemiology 22 (2011), pp. 859–866. doi: 10.1097/EDE.0b013e31822908b3
   PubMed Web of Science ®Google Scholar
• A. Cannon, Quantile regression neural networks: Implementation in R and application to precipitation downscaling, Comput. Geosci. 37 (2011), pp. 1277–1284. doi: 10.1016/j.cageo.2010.07.005
   Web of Science ®Google Scholar
• S.K. Chao, W.K. Härdle, and C. Huang, Multivariate factorizable expectile regression with application to fMRI data, Comput. Stat. Data. Anal. 121 (2018), pp. 1–19. doi: 10.1016/j.csda.2017.12.001
   Web of Science ®Google Scholar
• J.M. Chen, On exactitude in financial regulation: Value-at-Risk, expected shortfall, and expectiles, Risks 6 (2018), pp. 1–29. doi: 10.3390/risks6020061
   Web of Science ®Google Scholar
• G. Ciuperca, Variable selection in high-dimensional linear model with possibly asymmetric or heavy-tailed errors, Tech. rep., Universit Lyon 1 (2018).
   Google Scholar
• A. Daouia, S. Girard, and G. Stupfler, Estimation of tail risk based on extreme expectiles, J. R. Stat. Soc. Ser. B 80 (2018), pp. 263–292. doi: 10.1111/rssb.12254
   Google Scholar
• A. de Pierrefeu, T. Löfstedt, F. Hadj-Selem, M. Dubois, R. Jardri, T. Fovet, P. Ciuciu, V. Frouin, and E. Duchesnay, Structured sparse principal components analysis with the TV-elastic net penalty, IEEE. Trans. Med. Imaging. 37 (2018), pp. 396–407. doi: 10.1109/TMI.2017.2749140
   PubMed Web of Science ®Google Scholar
• J. Durbin, Testing for serial correlation in least-squares regression when some of the regressors are lagged dependent variables, Econometrica 38 (1970), pp. 410–421. doi: 10.2307/1909547
   Web of Science ®Google Scholar
• B. Efron, T. Hastie, I. Johnstone, and R. Tibshirani, Least angle regression, Ann. Stat. 32 (2004), pp. 407–499. doi: 10.1214/009053604000000067
   Web of Science ®Google Scholar
• W. Ehm, T. Gneiting, A. Jordan, and F. Krüger, Of quantiles and expectiles: Consistent scoring functions, choquet representations and forecast rankings, J. Royal Statist. Soc. B 78 (2016), pp. 505–562. doi: 10.1111/rssb.12154
   Google Scholar
• R. Engle and S. Manganelli, CAViaR: conditional autoregressive value at risk by regression quantiles, J. Business Econom. Stat. 22 (2004), pp. 367–381. doi: 10.1198/073500104000000370
   Web of Science ®Google Scholar
• J. Fan, Y. Fan, and E. Barut, Adaptive robust variable selection, Ann. Statist. 42 (2012), pp. 324–351. doi: 10.1214/13-AOS1191
   Web of Science ®Google Scholar
• J. Fan and R. Li, Variable selection via nonconcave penalized likelihood and its oracle properties, J. Am. Stat. Assoc. 96 (2001), pp. 1348–1360. doi: 10.1198/016214501753382273
   Web of Science ®Google Scholar
• M. Farooq and I. Steinwart, An SVM-like approach for expectile regression, Computat. Statist. Data Analysis 109 (2017), pp. 159–181. doi: 10.1016/j.csda.2016.11.010
   Web of Science ®Google Scholar
• N. Fenske, T. Kneib, and T. Hothorn, Identifying risk factors for severe childhood malnutrition by boosting additive quantile regression, J. Am. Stat. Assoc. 106 (2011), pp. 494–510. doi: 10.1198/jasa.2011.ap09272
   Web of Science ®Google Scholar
• J. Friedman, T. Hastie, and R. Tibshirani, Pathwise coordinate optimization, Ann. Appl. Stat. 1 (2007), pp. 302–332. doi: 10.1214/07-AOAS131
   Web of Science ®Google Scholar
• J. Friedman, T. Hastie, and R. Tibshirani, Pathwise coordinate optimization, J. Stat. Softw. 33 (2010), pp. 1–22. doi: 10.18637/jss.v033.i01
   PubMed Web of Science ®Google Scholar
• D.R. Goldstein, Analyzing microarray gene expression data, J. Am. Stat. Assoc. 100 (2005), pp. 1464–1465. doi: 10.1198/jasa.2005.s60
   Google Scholar
• M. González, D. Dominguez, and Á. Sánchez, Increase attractor capacity using an ensembled neural network, Expert. Syst. Appl. 71 (2017), pp. 206–215. doi: 10.1016/j.eswa.2016.11.035
   Web of Science ®Google Scholar
• C. Gouriéroux and J. Jasiak, Dynamic quantile models, J. Econom. 147 (2008), pp. 198–205. doi: 10.1016/j.jeconom.2008.09.028
   Web of Science ®Google Scholar
• Y. Gu and H. Zou, High-dimensional generalizations of asymmetric least squares regression and their applications, Ann. Statist. 44 (2016), pp. 2661–2694. doi: 10.1214/15-AOS1431
   Web of Science ®Google Scholar
• K. Guler, P.T. Ng, and Z. Xiao, Mincerczarnowitz quantile and expectile regressions for forecast evaluations under aysmmetric loss functions, J. Forecast. 36 (2017), pp. 651–679. doi: 10.1002/for.2462
   Web of Science ®Google Scholar
• B. Hamidi, B. Maillet, and J.L. Prigent, A dynamic autoregressive expectile for time-invariant portfolio protection strategies, J. Econom. Dyn. Control 46 (2014), pp. 1–29. doi: 10.1016/j.jedc.2014.05.005
   Web of Science ®Google Scholar
• A.E. Hoerl, R.W. Kennard, and R.W. Hoerl, Practical use of ridge regression: A challenge met, J. R. Stat. Soc. Ser. C 34 (1985), pp. 114–120.
   Web of Science ®Google Scholar
• P.J. Huber, Robust regression: Asymptotics, conjectures and monte carlo, Ann. Stat. 1 (1973), pp. 799–821. doi: 10.1214/aos/1176342503
   Web of Science ®Google Scholar
• C. Jiang, M. Jiang, Q. Xu, and X. Huang, Expectile regression neural network model with applications, Neurocomputing 247 (2017), pp. 73–86. doi: 10.1016/j.neucom.2017.03.040
   Web of Science ®Google Scholar
• M.C. Jones, Expectiles and M-quantiles are quantiles, Stat. Probab. Lett. 20 (1994), pp. 149–153. doi: 10.1016/0167-7152(94)90031-0
   Web of Science ®Google Scholar
• M. Kim and S. Lee, Nonlinear expectile regression with application to Value-at-Risk and expected shortfall estimation, Comput. Stat. Data Anal. 94 (2016), pp. 1–19. doi: 10.1016/j.csda.2015.07.011
   Web of Science ®Google Scholar
• R. Koenker, Additive models for quantile regression: Model selection and confidence bandaids, Brazilian J. Probab. Stat. 25 (2011), pp. 239–262. doi: 10.1214/10-BJPS131
   Web of Science ®Google Scholar
• R. Koenker and G.W. Bassett Jr, Regression quantiles, Econometrica 46 (1978), pp. 33–50. doi: 10.2307/1913643
   Web of Science ®Google Scholar
• R. Koenker, P. Ng, and S. Portnoy, Quantile smoothing splines, Biometrika 81 (1994), pp. 673–680. doi: 10.1093/biomet/81.4.673
   Web of Science ®Google Scholar
• C.M. Kuan, J.H. Yeh, and Y.C. Hsu, Assessing value at risk with CARE, the conditional autoregressive expectile models, J. Econom. 150 (2009), pp. 261–270. doi: 10.1016/j.jeconom.2008.12.002
   Web of Science ®Google Scholar
• C. Lamarche, Robust penalized quantile regression estimation for panel data, J. Econom. 157 (2010), pp. 396–408. doi: 10.1016/j.jeconom.2010.03.042
   Web of Science ®Google Scholar
• Y. Li, Y. Liu, and J. Zhu, Quantile regression in reproducing kernel hilbert spaces, J. Am. Stat. Assoc. 102 (2007), pp. 255–268. doi: 10.1198/016214506000000979
   Web of Science ®Google Scholar
• Q. Li, R. Xi, and N. Lin, Bayesian regularized quantile regression, Bayesian Anal. 5 (2010), pp. 533–556. doi: 10.1214/10-BA521
   Web of Science ®Google Scholar
• S. Li and W. Ye, A generalized elastic net regularization with smoothed l0 penalty, Adv. Pure Math. 7 (2017), pp. 66–74. doi: 10.4236/apm.2017.71006
   Google Scholar
• Y. Li and J. Zhu, L1-norm quantile regression, J. Comput. Graph. Stat. 17 (2008), pp. 163–185. doi: 10.1198/106186008X289155
   Web of Science ®Google Scholar
• H. Lian, Semiparametric estimation of additive quantile regression models by two-fold penalty, J. Bus. Econ. Stat. 30 (2012), pp. 337–350. doi: 10.1080/07350015.2012.693851
   Web of Science ®Google Scholar
• L. Liao, C. Park, and H. Choi, Penalized expectile regression: An alternative to penalized quantile regression, Ann. Inst. Stat. Math. 71 (2019), pp. 409–438. doi: 10.1007/s10463-018-0645-1
   Web of Science ®Google Scholar
• J. Liu, J. Huang, and S. Ma, Integrative analysis of multiple cancer genomic datasets under the heterogeneity model, Stat. Med. 32 (2013), pp. 3509–3521. doi: 10.1002/sim.5780
   PubMed Web of Science ®Google Scholar
• A. Mkhadri, M. Ouhourane, and K. Oualkacha, A coordinate descent algorithm for computing penalized smooth quantile regression, Stat. Comput. 27 (2017), pp. 865–883. doi: 10.1007/s11222-016-9659-9
   Web of Science ®Google Scholar
• W.K. Newey and J.L. Powell, Asymmetric least squares estimation and testing, Econometrica 55 (1987), pp. 819–847. doi: 10.2307/1911031
   Web of Science ®Google Scholar
• J. Niu, J. Chen, and Y. Xu, Twin support vector regression with huber loss, J. Intel. Fuzzy Syst. 32 (2017), pp. 4247–4258. doi: 10.3233/JIFS-16629
   Web of Science ®Google Scholar
• J. Pecanka, A.W. van der Vaart, and M.A. Jonker, Modeling association between multivariate correlated outcomes and high-dimensional sparse covariates: The adaptive SVS method, J. Appl. Stat. 46 (2019), pp. 893–913. doi: 10.1080/02664763.2018.1523377
   Web of Science ®Google Scholar
• B. Peng and L. Wang, An iterative coordinate descent algorithm for high-dimensional nonconvex penalized quantile regression, J. Comput. Graph. Stat. 24 (2015), pp. 676–694. doi: 10.1080/10618600.2014.913516
   Web of Science ®Google Scholar
• L. Qi and J. Sun, A nonsmooth version of newton's method, Math. Program. 58 (1993), pp. 353–367. doi: 10.1007/BF01581275
   Web of Science ®Google Scholar
• J.D. Sargan and A. Bhargava, Testing residuals from least squares regression for being generated by the Gaussian random walk, Econometrica 51 (1983), pp. 153–174. doi: 10.2307/1912252
   Web of Science ®Google Scholar
• L. Schulze Waltrup and G. Kauermann, Smooth expectiles for panel data using penalized splines, Stat. Comput. 27 (2017), pp. 271–282. doi: 10.1007/s11222-015-9621-2
   Web of Science ®Google Scholar
• Y. Shen, H.Y. Liang, and G.L. Fan, Penalized empirical likelihood for quantile regression with missing covariates and auxiliary information, Commun. Stat. Theory Methods 47 (2018), pp. 2001–2021. doi: 10.1080/03610926.2017.1335413
   Web of Science ®Google Scholar
• N. Simon, J. Friedman, T. Hastie, and R. Tibshirani, Regularization paths for Cox's proportional hazards model via coordinate descent, J. Stat. Softw. 39 (2011), pp. 1–13. doi: 10.18637/jss.v039.i05
   PubMed Web of Science ®Google Scholar
• F. Sobotka, G. Kauermann, L.S. Waltrup, and T. Kneib, On confidence intervals for semiparametric expectile regression, Stat. Comput. 23 (2013), pp. 135–148. doi: 10.1007/s11222-011-9297-1
   Web of Science ®Google Scholar
• F. Sobotka and T. Kneib, Geoadditive expectile regression, Comput. Stat. Data Anal. 56 (2012), pp. 755–767. doi: 10.1016/j.csda.2010.11.015
   Web of Science ®Google Scholar
• E. Spiegel, T. Kneib, and F. Otto-Sobotka, Spatio-temporal expectile regression models, Statist. Model. (2019).
   Google Scholar
• E. Spiegel, F. Sobotka, and T. Kneib, Model selection in semiparametric expectile regression, Electron. J. Stat. 11 (2017), pp. 3008–3038. doi: 10.1214/17-EJS1307
   Web of Science ®Google Scholar
• J.W. Taylor, Estimating value at risk and expected shortfall using expectiles, J. Financial Econom. 6 (2008), pp. 231–252. doi: 10.1093/jjfinec/nbn001
   Web of Science ®Google Scholar
• R. Tibshirani, Regression shrinkage and selection via the lasso, J. R. Stat. Soc. Ser. B 58 (1996), pp. 267–288.
   Google Scholar
• P. Tseng, Convergence of a block coordinate descent method for nondifferentiable minimization, J. Optim. Theory Appl. 109 (2001), pp. 475–494. doi: 10.1023/A:1017501703105
   Web of Science ®Google Scholar
• E. Waldmann, F. Sobotka, and T. Kneib, Bayesian geoadditive expectile regression, Comput. Stat. Data Anal. 56 (2013), pp. 755–767.
   Web of Science ®Google Scholar
• E. Waldmann, F. Sobotka, and T. Kneib, Bayesian regularisation in geoadditive expectile regression, Stat. Comput. 27 (2017), pp. 1539–1553. doi: 10.1007/s11222-016-9703-9
   Web of Science ®Google Scholar
• M.A. Walker, I. Langkilde-Geary, H.W. Hastie, J. Wright, and A. Gorin, Automatically training a problematic dialogue predictor for a spoken dialogue system, J. Artificial Intel. Res. 16 (2002), pp. 293–319. doi: 10.1613/jair.971
   Web of Science ®Google Scholar
• L.S. Waltrup, F. Sobotka, T. Kneib, and G. Kauermann, Expectile and quantile regressiondavid and goliath? Stat. Model. 15 (2015), pp. 433–456. doi: 10.1177/1471082X14561155
   Web of Science ®Google Scholar
• L. Wang, I.V. Keilegom, and A. Maidman, Wild residual bootstrap inference for penalized quantile regression with heteroscedastic errors, Biometrika 105 (2018), pp. 859–872. doi: 10.1093/biomet/asy037
   Web of Science ®Google Scholar
• H. Wang and C. Leng, A note on adaptive group lasso, Comput. Stat. Data Anal. 52 (2008), pp. 5277–5286. doi: 10.1016/j.csda.2008.05.006
   Web of Science ®Google Scholar
• X. Wang and M. Wang, Variable selection for high-dimensional generalized linear models with the weighted elastic-net procedure, J. Appl. Stat. 43 (2016), pp. 796–809. doi: 10.1080/02664763.2015.1078300
   Web of Science ®Google Scholar
• N. Wirsik, F. Otto-Sobotka, and I. Pigeot, Modeling physical activity data using L0-penalized expectile regression, Biometrical J. 61 (2019), pp. 1371–1384. doi: 10.1002/bimj.201800007
   PubMed Web of Science ®Google Scholar
• S. Wold, A. Ruhe, H. Wold, and W.J. Dunn III, The collinearity problem in linear regression. The partial least squares (PLS) approach to generalized inverses, SIAM J. Sci. Stat. Comput. 5 (1984), pp. 735–743. doi: 10.1137/0905052
   Web of Science ®Google Scholar
• Y. Wu and Y. Liu, Variable selection in quantile regression, Stat. Sin. 19 (2009), pp. 801–817.
   Web of Science ®Google Scholar
• T. Wu, K. Yu, and Y. Yu, Single-index quantile regression, J. Multivar. Anal. 101 (2010), pp. 1607–1621. doi: 10.1016/j.jmva.2010.02.003
   Web of Science ®Google Scholar
• S. Xie, Y. Zhou, and A.T.K. Wan, A varying-coefficient expectile model for estimating value at risk, J. Bus. Econ. Stat. 32 (2014), pp. 576–592. doi: 10.1080/07350015.2014.917979
   Web of Science ®Google Scholar
• Q. Xu, C. Cai, C. Jiang, F. Sun, and X. Huang, Sampling lasso quantile regression for large-scale data, Commun. Stat. Simulat. Comput. 47 (2018), pp. 92–114. doi: 10.1080/03610918.2016.1277750
   Web of Science ®Google Scholar
• Q. Xu, X. Liu, C. Jiang, and K. Yu, Nonparametric conditional autoregressive expectile model via neural network with applications to estimating financial risk, Appl. Stoch. Models. Bus. Ind. 32 (2016), pp. 882–908. doi: 10.1002/asmb.2212
   Web of Science ®Google Scholar
• Y. Yang, T. Zhang, and H. Zou, Flexible expectile regression in reproducing kernel Hilbert spaces, Technometrics 60 (2018), pp. 26–35. doi: 10.1080/00401706.2017.1291450
   Web of Science ®Google Scholar
• Y. Yang and H. Zou, An efficient algorithm for computing the HHSVM and its generalizations, J. Comput. Graphical Stat. 22 (2013), pp. 396–415. doi: 10.1080/10618600.2012.680324
   Web of Science ®Google Scholar
• Y. Yang and H. Zou, Nonparametric multiple expectile regression via ER-Boost, J. Stat. Comput. Simul. 85 (2015), pp. 1442–1458. doi: 10.1080/00949655.2013.876024
   Web of Science ®Google Scholar
• Q. Yao and H. Tong, Asymmetric least squares regression estimation: A nonparametric approach, J. Nonparametr. Stat. 6 (1996), pp. 273–292. doi: 10.1080/10485259608832675
   Google Scholar
• C. Yi and J. Huang, Semismooth newton coordinate descent algorithm for elastic-net penalized huber loss regression and quantile regression, J. Comput. Graph. Stat. 26 (2017), pp. 547–557. doi: 10.1080/10618600.2016.1256816
   Web of Science ®Google Scholar
• K. Yu and M. Jones, Local linear quantile regression, J. Am. Stat. Assoc. 93 (1998), pp. 228–237. doi: 10.1080/01621459.1998.10474104
   Web of Science ®Google Scholar
• M. Yuan and Y. Lin, Model selection and estimation in regression with grouped variables, J. R. Stat. Soc. Ser. B 68 (2006), pp. 49–67. doi: 10.1111/j.1467-9868.2005.00532.x
   Google Scholar
• C.H. Zhang, Nearly unbiased variable selection under minimax concave penalty, Ann. Stat. 38 (2010), pp. 894–942. doi: 10.1214/09-AOS729
   Web of Science ®Google Scholar
• J. Zhao, Y. Chen, and Y. Zhang, Expectile regression for analyzing heteroscedasticity in high dimension, Stat. Probab. Lett. 137 (2018), pp. 304–311. doi: 10.1016/j.spl.2018.02.006
   Web of Science ®Google Scholar
• J. Zhao, G. Yan, and Y. Zhang, Semiparametric expectile regression for high-dimensional heavy-tailed and heterogeneous data, Tech. rep., Zhejiang University City College (2019)
   Google Scholar
• J. Zhao and Y. Zhang, Variable selection in expectile regression, Commun. Stat. Theory Methods 47 (2018), pp. 1731–1746. doi: 10.1080/03610926.2017.1324989
   Web of Science ®Google Scholar
• H. Zou, The adaptive lasso and its oracle properties, J. Am. Stat. Assoc. 101 (2006), pp. 1418–1429. doi: 10.1198/016214506000000735
   Web of Science ®Google Scholar
• H. Zou and T. Hastie, Regularization and variable selection via the elastic net, J. R. Stat. Soc. Ser. B 67 (2005), pp. 301–320. doi: 10.1111/j.1467-9868.2005.00503.x
   Google Scholar
• H. Zou and M. Yuan, Composite quantile regression and the oracle model selection theory, Ann. Stat. 36 (2008), pp. 1108–1126. doi: 10.1214/07-AOS507
   Web of Science ®Google Scholar