Empirical likelihood for quantile regression models with longitudinal data

We develop two empirical likelihood-based inference procedures for longitudinal data under the framework of quantile regression. The proposed methods avoid estimating the unknown error density function and the intra-subject correlation involved in the asymptotic covariance matrix of the quantile estimators. By appropriately smoothing the quantile score function, the empirical likelihood approach is shown to have a higher-order accuracy through the Bartlett correction. The proposed methods exhibit finite-sample advantages over the normal approximation-based and bootstrap methods in a simulation study and the analysis of a longitudinal ophthalmology data set.

[1]  A. Owen.  Empirical likelihood ratio confidence intervals for a single functional , 1988 .

[2]  Using empirical likelihood methods to obtain range restricted weights in regression estimators for surveys , 2002 .

[3]  Hengjian Cui,et al.  On Bartlett correction of empirical likelihood in the presence of nuisance parameters , 2006 .

[4]  M. Bottai,et al.  Quantile regression for longitudinal data using the asymmetric Laplace distribution. , 2007, Biostatistics.

[5]  J. Horowitz.  Bootstrap Methods for Median Regression Models , 1996 .

[6]  Lixing Zhu,et al.  Empirical Likelihood for a Varying Coefficient Model With Longitudinal Data , 2007 .

[7]  Lee-Jen Wei,et al.  Quantile Regression for Correlated Observations , 2004 .

[8]  P X Song,et al.  Marginal Models for Longitudinal Continuous Proportional Data , 2000, Biometrics.

[9]  Wu.  Using empirical likelihood methods to obtain range restricted weights in regression estimators for surveys , 2002 .

[10]  B. M. Brown,et al.  Standard errors and covariance matrices for smoothed rank estimators , 2005 .

[11]  R. Koenker,et al.  Regression Quantiles , 2007 .

[12]  P. McCullagh.  Tensor Methods in Statistics , 1987 .

[13]  Yoon-Jae Whang,et al.  SMOOTHED EMPIRICAL LIKELIHOOD METHODS FOR QUANTILE REGRESSION MODELS , 2004, Econometric Theory.

[14]  Peter Hall,et al.  Smoothed empirical likelihood confidence intervals for quantiles , 1993 .

[15]  S. Lipsitz,et al.  Quantile Regression Methods for Longitudinal Data with Drop‐outs: Application to CD4 Cell Counts of Patients Infected with the Human Immunodeficiency Virus , 1997 .

[16]  Taisuke Otsu,et al.  Conditional empirical likelihood estimation and inference for quantile regression models , 2008 .

[17]  Xiao-Hua Zhou,et al.  Estimating the retransformed mean in a heteroscedastic two-part model , 2006 .

[18]  Feiming Chen,et al.  Empirical likelihood inference for censored median regression model via nonparametric kernel estimation , 2008 .

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

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

[21]  Min Zhu,et al.  Quantile regression without the curse of unsmoothness , 2009, Comput. Stat. Data Anal..

[22]  Min Tsao,et al.  Empirical likelihood inference for median regression models for censored survival data , 2003 .

[23]  Sundarraman Subramanian.  Censored Median Regression and Profile Empirical Likelihood. , 2007, Statistical methodology.

[24]  Q. Shao,et al.  A general bahadur representation of M-estimators and its application to linear regression with nonstochastic designs , 1996 .

[25]  Mai Zhou,et al.  RESEARCH ARTICLE Empirical Likelihood Analysis for the Heteroscedastic Accelerated Failure Time Model , 2008 .

[26]  Sin-Ho Jung.  Quasi-Likelihood for Median Regression Models , 1996 .

[27]  Song Xi Chen,et al.  Smoothed Block Empirical Likelihood for Quantiles of Weakly Dependent Processes , 2006 .

[28]  Qian Yong-jiang.  Empirical Likelihood Ratio Confidence Regions for Dependent Samples , 2008 .

[29]  Jianwen Cai,et al.  Quantile Regression Models with Multivariate Failure Time Data , 2005, Biometrics.

[30]  Thomas J. DiCiccio,et al.  Empirical Likelihood is Bartlett-Correctable , 1991 .