On the Equivariance of Location Reparameterization of Quantile Regression Model using Cauchy Transformation

Abstract

Often times fine-tuning the location parameter of original variables or reparameterizing a model in order to make the result obtained from such change to have an improved natural interpretation is desirable. Based on the regression output such changes are expected to affect either the qualitative and quantitative conclusion. This article tends to examine the equivariance to location reparameterization of quantile regression model. The analysis was done using real life data set on fuel consumption (in miles per gallon), in highway driving as the response variable while car weight, length, wheel base, width, Engine size and horse power are the explanatory variables with a sample size of 91. The general Cauchy distribution was used to transform the quantile regression model. The results show that mean square errors from the quantile regression model estimates are similar across different location parameters of our study model; this therefore shows that quantile regression model has the property of equivariance to location reparameterization.

Keywords: Quantile Regression Model, Cauchit Quantile Regression Model, location Reparameterization and Mean Square Error