### Scaled Box-Cox Quantile Regression Using the Geometric Mean as The Scaling Factor

#### Abstract

*Box-Cox transformation since its proposal has been modified by many authors. It was extended to quantile regression as Box-Cox quantile regression. An option of Box-Cox transformation that doesn’t appear to have been explored much in literature is the scaled Box-Cox transformation. This study extends the Box-Cox quantile regression to accommodate scaling of the response variable using the geometric mean as the scaling factor. A simulation study demonstrates that the scaled quantile regression estimator works well in situations, where the sample size is small as well as in the mid-quantiles of large samples in comparison to the original Box-Cox quantile regression estimator. The study also demonstrates that in very large sample sizes both estimators performed in a similar manner. An empirical example was also used.*

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