Journal
MATHEMATICS
Volume 9, Issue 10, Pages -Publisher
MDPI
DOI: 10.3390/math9101138
Keywords
Box-Cox transformation; quantile regression; relative error
Categories
Funding
- National Natural Science Foundation of China [11901013]
- Beijing Natural Science Foundation [1204031]
- Fundamental Research Funds for the Central Universities
- Beijing Talent Foundation Outstanding Young Individual Project
- Academy for Multidisciplinary Studies of Capital Normal University
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Motivated by the relative loss estimator of the median, a new class of estimators for linear quantile models is proposed using a general relative loss function. The proposed estimator is shown to have smaller variance and be more efficient than traditional linear quantile estimator. Simulation studies and application in a prostate cancer study demonstrate good performance of the proposed method.
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.
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