Some simulation studies and a real data application are undertaken to assess the finite sample performance of the proposed variable selection methods, and simulation results indicate that the proposed variable selection methods are workable.
📌 3 Maddede Bu Makale
🎯
Amaç & Hipotez:In this paper, we consider variable selection for partially linear quantile regression models with missing response at random.
📊
Temel Bulgular & Veri:We first propose a role penalized empirical likelihood based variable selection method, and show that such variable selection method is consistent and satisfies sparsity.
💡
Sonuç & Katkı:Some simulation studies and a real data application are undertaken to assess the finite sample performance of the proposed variable selection methods, and simulation results indicate that the proposed variable selection methods are workable.
🔬Tür:Modelleme & Sayısal Simülasyon
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Quantile regression · Partially linear model · Variable selection
Abstract
In this paper, we consider variable selection for partially linear quantile regression models with missing response at random. We first propose a role penalized empirical likelihood based variable selection method, and show that such variable selection method is consistent and satisfies sparsity. Further more, to avoid the influence of nonparametric estimator on the variable selection for the parametric components, we also propose a double penalized empirical likelihood variable selection method. Some simulation studies and a real data application are undertaken to assess the finite sample performance of the proposed variable selection methods, and simulation results indicate that the proposed variable selection methods are workable.
TANG, X., ZHAO, P. (2022). Penalized empirical likelihood based variable selection for partially linear quantile regression models with missing responses. Hacettepe Journal of Mathematics and Statistics, Cilt: 47 - Sayı: 3, 721–739. https://ajindex.com/articles/529870
Koenker, R. and Bassett, G.S. Regression quantiles, Econometrica 46, 33-50, 1978.
Buchinsky, M. Recent advances in quantile regression models: A practical guide for empir- ical research, Journal of Human Resources 33, 88-126, 1998.
Koenker, R. and Machado, J. Goodness of t and related inference processes for quantile regression, Journal of the American Statistical Association 94, 1296-1310, 1999.
Tang, C.Y. and Leng, C.L. An empirical likelihood approach to quantile regression with auxiliary information, Statistics & Probability Letters 82, 29-36, 2012.
Hendricks, W. and Koenker, R. Hierarchical spline models for conditional quantiles and the demand for electricity, Journal of the American Statistical Association 87, 58-68, 1992.
Yu, K. and Jones, M.C. Local linear quantile regression, Journal of The American Statistical Association 93, 228-237, 1998.
Dabrowska, D.M. Nonparametric quantile regression with censored data, The Indian Journal of Statistics, Series A 54, 252-259, 1992.
Lee, S. E cient semiparametric estimation of a partially linear quantile regression model, Econometric Theory 19, 1-31, 2003.
Sun, Y. Semiparametric e cient estimation of partially linear quantile regression models, The Annals of Economics and Finance 6, 105-127, 2005.
He, X. and Liang, H. Quantile regression estimates for a class of linear and partially linear errors-in-variables models, Statistica Sinica 10, 129-140, 2000.
Chen, S. and Khan, S. Semiparametric estimation of a partially linear censored regression model, Economic Theory 17, 567-590, 2001.
Lv, X. and Li, R. Smoothed empirical likelihood analysis of partially linear quantile regres- sion models with missing response variables, Advances in Statistical Analysis 97, 317-347, 2013.
Tang, C.Y. and Leng, C. Penalized high-dimensional empirical likelihood, Biometrika 97, 905-920, 2010.
Ren, Y.W. and Zhang, X.S. Variable selection using penalized empirical likelihood, Science China Mathematics 54, 1829-1845, 2011.
Variyath, A.M., Chen, J. and Abraham, B. Empirical likelihood based variable selection, Journal of Statistical Planning and Inference 140, 971-981, 2010.
Wu, T.T., Li, G. and Tang, C. Empirical likelihood for censored linear regression and vari- able selection, Scandinavian Journal of Statistics 42, 798-812, 2015.
Zhao, P. X. Empirical likelihood based variable selection for varying coe cient partially linear models with censored data, Journal of Mathematical Research with Applications 33, 493-504, 2013.