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

• Main Authors: Tao Hu, Baosheng Liang
• Format: Article
• Language: English
• Published: MDPI AG 2021-05-01
• Series: Mathematics
• Subjects: Box–Cox transformation; quantile regression; relative error
• Online Access: https://www.mdpi.com/2227-7390/9/10/1138

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 statistical 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.