A New Class of Estimators Based on a General Relative Loss Function

Tao Hu, Baosheng Liang
2021 Mathematics  
Motivated by the relative loss estimator of the median, we propose a new class of estimators for linear quantile models using a general relative loss function defined by the Box–Cox transformation function. The proposed method is very flexible. It includes a traditional quantile regression and median regression under the relative loss as special cases. Compared to the traditional linear quantile estimator, the proposed estimator has smaller variance and hence is more efficient in making
more » ... cal inferences. We show that, in theory, the proposed estimator is consistent and asymptotically normal under appropriate conditions. Extensive simulation studies were conducted, demonstrating good performance of the proposed method. An application of the proposed method in a prostate cancer study is provided.
doi:10.3390/math9101138 fatcat:ddepjsj7yvf2nfdjexszpexmo4