Sheep in Wolf’s Clothing: Using the Least Squares Criterion for Quantile Estimation

Estimation of the quantile model, especially with a large data set, can be computationally burdensome. This paper proposes using the Gaussian approximation, also known as quantile coupling, to estimate a quantile model. The intuition of quantile coupling is to divide the original observations into bins with an equal number of observations, and then compute order statistics within these bins. The quantile coupling allows one to apply the standard Gaussian-based estimation and inference to the transformed data set. The resulting estimator is asymptotically normal with a parametric convergence rate. A key advantage of this method is that it is faster than the conventional check function approach, when handling a sizable data set.