Improved multiple quantile regression estimation with nonignorable dropouts

• Published in: Journal of the Korean Statistical Society Vol. 52; no. 1; pp. 1 - 32
• Main Authors: Ma, Wei, Zhang, Ting, Wang, Lei
• Format: Journal Article
• Language: English
• Published: Singapore Springer Nature Singapore 01.03.2023
• Subjects: Applied Statistics; Bayesian Inference; Mathematics and Statistics; Research Article; Statistical Theory and Methods; Statistics; Statistics and Computing/Statistics Programs; Within-subject correction; Quadratic inference function; Nonignorable dropout; Smoothed empirical likelihood
• ISSN: 1226-3192; 2005-2863
• DOI: 10.1007/s42952-022-00185-1

This paper proposes an efficient approach to deal with the issue of estimating multiple quantile regression (MQR) model. The relationship between the multiple quantiles and within-subject correlation is accommodated to improve efficiency in the presence of nonignorable dropouts. We adopt empirical likelihood (EL) to estimate the MQR coefficients. To handle the identifiability issue caused by nonignorable dropouts, a nonresponse instrument is used to estimate the parameters involved in a propensity model. In addition, bias-corrected and smoothed generalized estimating equations are built by applying kernel smoothing and inverse probability weighting approach. Furthermore, in order to measure the within-subject correlation structure, the idea of quadratic inference function is also taken into account. Theoretical results indicate that the proposed estimator has asymptotic normality and the confidence regions for MQR coefficients are also derived. Numerical simulations and an application to real data are also presented to investigate the performance of our proposed method.