Weighted quantile regression in varying-coefficient model with longitudinal data

A weighted approach is developed to improve estimation efficiency in varying-coefficient quantile regression model, with longitudinal data. The weights are obtained from empirical likelihood of varying-coefficient mean model, where the nonparametric functions are approximated by basis splines, and the matrix expansion idea in quadratic inference function method is used, to model the inverse of conditional correlation matrix within subject. Theoretical results show that, the weighted estimators of the varying coefficients in quantile regression, can achieve higher efficiency than conventional estimators without weighting scheme. Simulation studies are used to assess the finite sample performance and a real data analysis is also conducted.

[1]  Liya Fu,et al.  Quantile regression for longitudinal data with a working correlation model , 2012, Comput. Stat. Data Anal..

[2]  Guang Cheng,et al.  Quantile Processes for Semi and Nonparametric Regression , 2016, 1604.02130.

[3]  Raymond J. Carroll,et al.  A SIMULTANEOUS CONFIDENCE BAND FOR SPARSE LONGITUDINAL REGRESSION , 2012 .

[4]  Runze Li,et al.  Analysis of Longitudinal Data With Semiparametric Estimation of Covariance Function , 2007, Journal of the American Statistical Association.

[5]  Mi-Ok Kim,et al.  Semiparametric Approach to a Random Effects Quantile Regression Model , 2011, Journal of the American Statistical Association.

[6]  Yanlin Tang,et al.  Improving estimation efficiency in quantile regression with longitudinal data , 2015 .

[7]  R. Koenker.  Quantile regression for longitudinal data , 2004 .

[8]  Hyunkeun Cho,et al.  Efficient estimation in the partially linear quantile regression model for longitudinal data , 2018 .

[9]  Zhongyi Zhu,et al.  Estimation in a semiparametric model for longitudinal data with unspecified dependence structure , 2002 .

[10]  Huixia Judy Wang.  INFERENCE ON QUANTILE REGRESSION FOR HETEROSCEDASTIC MIXED MODELS , 2009 .

[11]  Runze Li,et al.  Quadratic Inference Functions for Varying‐Coefficient Models with Longitudinal Data , 2006, Biometrics.

[12]  Jianhui Zhou,et al.  Quantile regression in partially linear varying coefficient models , 2009, 0911.3501.

[13]  Q. Shao,et al.  On Parameters of Increasing Dimensions , 2000 .

[14]  H. Bondell,et al.  Flexible Bayesian quantile regression for independent and clustered data. , 2010, Biostatistics.

[15]  Mi-Ok Kim,et al.  Quantile regression with varying coefficients , 2007, 0708.0471.

[16]  Zongwu Cai,et al.  Nonparametric Quantile Estimations for Dynamic Smooth Coefficient Models , 2008 .

[17]  Victor Chernozhukov,et al.  Conditional quantile processes based on series or many regressors , 2019, Journal of Econometrics.

[18]  Huixia Judy Wang,et al.  Variable selection in quantile varying coefficient models with longitudinal data , 2013, Comput. Stat. Data Anal..

[19]  Bin Chen,et al.  Empirical likelihood for high-dimensional linear regression models , 2014 .

[20]  Xiaotong Shen,et al.  Local asymptotics for regression splines and confidence regions , 1998 .

[21]  B. Lindsay,et al.  Improving generalised estimating equations using quadratic inference functions , 2000 .

[22]  J. Lawless,et al.  Empirical Likelihood and General Estimating Equations , 1994 .

[23]  Xingdong Feng,et al.  COPULA-BASED QUANTILE REGRESSION FOR LONGITUDINAL DATA , 2018 .

[24]  L. Schumaker.  Spline Functions: Basic Theory , 1981 .

[25]  R. Serfling.  Approximation Theorems of Mathematical Statistics , 1980 .

[26]  Chenlei Leng,et al.  Penalized empirical likelihood and growing dimensional general estimating equations , 2012 .

[27]  Chaohui Guo,et al.  Robust variable selection in high-dimensional varying coefficient models based on weighted composite quantile regression , 2017 .

[28]  Zhongyi Zhu,et al.  On the asymptotics of marginal regression splines with longitudinal data , 2008 .

[29]  Zhongyi Zhu,et al.  Empirical likelihood for quantile regression models with longitudinal data , 2011 .

[30]  Jianhua Z. Huang.  Local asymptotics for polynomial spline regression , 2003 .

[31]  Yong Zhou,et al.  Block empirical likelihood for longitudinal partially linear regression models , 2006 .

[32]  Chenlei Leng,et al.  Empirical likelihood and quantile regression in longitudinal data analysis , 2011 .

[33]  R. Carroll,et al.  Nonparametric Function Estimation for Clustered Data When the Predictor is Measured without/with Error , 2000 .

[34]  Weiping Zhang,et al.  Smoothing combined estimating equations in quantile regression for longitudinal data , 2014, Stat. Comput..