Empirical likelihood change point detection in quantile regression models

Quantile regression is an extension of linear regression which estimates a conditional quantile of interest. In this paper, we propose an empirical likelihood-based non-parametric procedure to detect structural changes in the quantile regression models. Further, we have modified the proposed smoothed empirical likelihood-based method using adjusted smoothed empirical likelihood and transformed smoothed empirical likelihood techniques. We have shown that under the null hypothesis, the limiting distribution of the smoothed empirical likelihood ratio test statistic is identical to that of the classical parametric likelihood. Simulations are conducted to investigate the finite sample properties of the proposed methods. Finally, to demonstrate the effectiveness of the proposed method, it is applied to urinary Glycosaminoglycans (GAGs) data to detect structural changes.