Smoothed empirical likelihood inference via the modified Cholesky decomposition for quantile varying coefficient models with longitudinal data

Abstract

It is essential to deal with the within-subject correlation among repeated measures over time to improve statistical inference efficiency. However, it is a challenging task to correctly specify a working correlation in quantile regression with longitudinal data. In this paper, we first develop an adaptive approach to estimate the within-subject covariance matrix of quantile regression by applying a modified Cholesky decomposition. Then, weighted kernel GEE-type quantile estimating equations are proposed for varying coefficient functions. Note that the proposed estimating equations include a discrete indicator function, which results in some problems for computation and asymptotic analysis. Thus, we construct smoothed estimating equations by introducing a bounded kernel function. Furthermore, we develop a smoothed empirical likelihood method to improve the accuracy of interval estimation. Finally, simulation studies and a real data analysis indicate that the proposed method has superior advantages over the existing methods in terms of coverage accuracies and widths of confidence intervals.