The single-index quantile regression model is an important semiparametric model with the merit of dimensionality reduction. Furthermore, it retains the robustness of a nonparametric model. For most existing estimating procedures of single-index quantile regression models, the estimators are obtained via minimizing the objective functions by the interior point method. In this paper, we investigate the MM (majorize-minimize) algorithm of the single index quantile regression model estimating procedure. We first construct the majorize function of the objective function and then minimize the substituted majorize function to find the estimators. Our numerical simulations and empirical study show that for the considered model, the MM algorithm has good stability and can yield more accurate estimation. Compared with the interior point method, the MM algorithm is more efficient and takes less time.
GUO Yuanyuan
,
YANG Xuemei
,
SUN Zhihua
. MM algorithm of the estimation of single-index quantile regression[J]. Journal of University of Chinese Academy of Sciences, 2021
, 38(3)
: 289
-296
.
DOI: 10.7523/j.issn.2095-6134.2021.03.001
[1] Zhao X, Wang W, Liu L, et al. A flexible quantile regression model for medical costs with application to Medical Expenditure Panel Survey Study[J]. Statistics in Medicine, 2018, 37(17):2645-2666.
[2] Petrella L, Raponi V. Joint estimation of conditional quantiles in multivariate linear regression models with an application to financial distress[J]. Journal of Multivariate Analysis, 2019, 173:70-84.
[3] Tan X Z, Gan T Y, Chen S, et al. Modeling distributional changes in winter precipitation of Canada using Bayesian spatiotemporal quantile regression subjected to different teleconnections[J]. Climate Dynamics, 2019, 52:2105-2124.
[4] Xu B, Lin B. Investigating the differences in CO2 emissions in the transport sector across Chinese provinces:evidence from a quantile regrssion model(Article)[J]. Journal of Cleaner Production, 2018, 27(175):109-122.
[5] 姜成飞. 分位数回归方法综述[J]. 科技信息, 2013, 30(25):185-240.
[6] He X, Zhu L X. A lack-of-fit test for quantile regression[J]. Journal of the American Statistical Association, 2003,98(464):1013-1022.
[7] Mercedes C A, César S S, Wenceslao G M. A lack-of-fit test for quantile regression models with high-dimensional covariates[J]. Computational Statistics and Data Analysis, 2015, 33(88):128-138.
[8] 关静. 分位数回归理论及其应用[D]. 天津:天津大学, 2009.
[9] 朱平芳, 张征宇. 无条件分位数回归:文献综述与应用实例[J]. 统计研究, 2012, 29(3):88-96.
[10] 陈建宝, 丁军军. 分位数回归技术综述[J]. 统计与信息论坛, 2008, 23(3):89-96.
[11] Gao J Y. Computation in quantile and composite quantile regression models with or without regularization[D]. Edmonton:University of Alberta, 2015.
[12] Hunter D R, Lange K. Quantile regression via an MM algorithm[J]. Journal of Computational and Graphical Statistics, 2000, 9(1):60-77.
[13] Wu T Z, Yu K M, Yu Y. Single-index quantitle regression[J]. Jornal of Multivariate Analysis, 2010, 40(101):1607-1621.
[14] Kong E F, Xia Y C. A single-index quantile regression model and its estimation[J]. Econometric Theory, 2012, 28(4):730-768.
[15] Kuruwita C N. Non-iterative estimation and variable selection in the single-index quantile regression model[J]. Communications in Statistics-Simulation and Computation, 2016, 45(10):3615-3628.
[16] Christou E. A Non-iterative method for fitting the single index quantile regression model with uncensored and censored data[D]. Pennsylvania:The Pennsylvania State University, 2016.
[17] Hu Y A, Gramacy R B, Lian H. Bayesian quantile regression for single-index models[J]. Statistics and Computing, 2013, 23(4):437-454.
[18] Alshaybawee T, Midi H, Alhamzawi R. Bayesian elastic net single index quantile regression[J]. Journal of Applied Statistics, 2017, 44(5):853-871.
[19] Jiang R, Qian W M, Zhou Z G. Weighted composite quantile regression for single-index models[J]. Jornal of Multivariate Analysis, 2016, 148:34-48.
[20] Liu H L, Yang H. Estimation and variable selection in single-index composite quantile regression[J]. Communications in Statistics-Simulation and Computation, 2017, 46(9):7022-7039.
[21] Zhong W, Zhu L P, Li R Z, et al. Regularized quantile regression and robust feature screening for single index models[J]. Statistica Sinica, 2016, 26(1):69-95.
[22] Jiang Y L. Nonparametric quantile regression models via majorization minimization-algorithm[J]. Statistics and Its Interface, 2014, 7(2):235-240.
[23] Xie S Y, Wan A T K, Zhou Y. Quantile regression methods with varying-coefficient models for censored data[J]. Computational Statistics and Data Analysis, 2015, 88:154-172.
[24] Chen Y L, Tang M L, Tian M Z. Semiparametric hierarchical composite quantile regression[J]. Communications in statistics:theory and methods, 2015, 50(4-6):996-1012.
[25] Lin W, Kulasekera K B. Indentifiability of single-index models and additive-index models[J]. Biometrica Jornal, 2007, 31(94):496-501.
[26] Chaudhuri P, Doksum K, Samarov A. On average derivative quantile regression[J]. Annals of Statistics, 1997, 25(2):715-744.
[27] Yu K M, Jones M C. Local linear quantile regression[J]. Journal of the American Statistic Association, 1998,93(441):228-237.
[28] Lv Y Z, Zhang R Q, Zhao W H, et al. Quantile regression and variable selection of partial linear single-index model[J]. Ann Inst Stat Math, 2015, 67(2):375-409.
[29] De Gooijer J G, Zerom D. On additive conditional quantiles with high-dimensional covariates[J]. Journal of the American Statistic Association, 2003, 98(116):135-146.
