Sheep in Wolf's clothing: Using the least squares criterion for quantile estimation

•We use the quantile coupling to estimate a quantile model.•The quantile coupling is to bin and compute the order statistics within these bins.•When handling a sizable data set, our method is faster than the conventional check function approach.

This paper proposes using the Gaussian approximation, also known as quantile coupling, to estimate a quantile model. 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. This method is faster than the conventional check function approach, when handling a sizable data set.